An Extensive Review of Leaching Models for the Forecasting and Integrated Management of Surface and Groundwater Quality

Abstract

The present study reviews leachate models useful for proactive and rehab actions to safeguard surface and subsurface soft water, which have become even more scarce. Integrated management plans of water basins are of crucial importance since intensively cultivated areas are adding huge quantities of fertilizers to the soil, affecting surface water basins and groundwater. Aquifers are progressively being nitrified on account of the nitrogen-based fertilizer surplus, rendering water for human consumption not potable. Well-tested solute leaching models, standalone or part of a model package, provide rapid site-specific estimates of the leaching potential of chemical agents, mostly nitrates, below the root zone of crops and the impact of leaching toward groundwater. Most of the models examined were process-based or conceptual approaches. Nonetheless, empirical prediction models, though rather simplistic and therefore not preferrable, demonstrate certain advantages, such as less demanding extensive calibration database information requirements, which in many cases are unavailable, not to mention a stochastic approach and the involvement of artificial intelligence (AI). Models were categorized according to the porous medium and agents to be monitored. Integrated packages of nutrient models are irreplaceable elements for extensive catchments to monitor the terrestrial nitrogen-balanced cycle and to contribute to policy making as regards soft water management.

1. Introduction

Surface and groundwater quality management is an issue of high priority in the EU. Nowadays, the scarcity of soft water of a high quality is a great concern for human wellbeing and the future economy. Nitrates Directive 91/676/EEC introduced actions for preventing the nitrate pollution of water bodies (surface and groundwater) for agricultural purposes, laying emphasis on promoting good farming practices [1]. The Water Directive (98/83/EC), followed up by EU Directive 2015/1787 with the amended Annexes II and III, introduced criteria for water quality intended for human consumption, including water monitoring on a regular basis, quality standards, and organoleptic and microbiological quality [2,3].

Nonetheless, an integral statutory water management policy was lacking in that certain period. That gap was bridged in 2000 by setting the Water Framework Directive (WFD), which brought to the front stage new concepts of environmental approaches with ‘Good ecological status’ (abbr. GES) and the concept of integrated management at the spatial unit of the ‘River Basin’ [4]. The WFD incorporates mechanisms to prioritize standards as a minimum level of chemical quality, regarding the detection of hazardous chemical agents. Within the well-predefined national river basin network, specific protection zones were to be designated in which stricter objectives should be applied on a local basis if required. The WFD incorporates a dynamic list of priority substances in the EU region which outlines the major risks and concurrently sets all necessary cost-effective measures to abate all anthropogenic impacts and sustain the good water status of both surface and groundwater [4].

As complementary legislation to the aforementioned WFD, Directive 2008/105/EC introduced Environmental Quality Standards (abbr. EQSs) in the water policy field [5]. Decision No 2455/2001/EC prioritized thirty-three (33) chemical substances in soft waters [6]. Directive 2013/39/EU amended the WFD and EQS requirements and adopted an updated, enlarged list of priority substances in published annexes [7]. Parameter monitoring and sampling is undertaken all year round.

European water quality legislation is based on the United Nation’s Integrated Methodological Framework and the deeper involvement of stakeholders is expected in the implementation of properly established river basin management plans towards water sustainability pathways. The former entails the issuing of Integrated Water Management Plans on a local and regional basis.

Innovative ideas for the utilization of water resources are promoted through funded European programs as a priority area (Horizon 2020, Interreg, etc.), based on legislation revision on the reuse of treated wastewater (industrial and domestic) for a variety of purposes, e.g., irrigation, peri-urban green and agriculture watering, water use for industrial needs, etc. [8,9].

In EU countries, numerous agricultural activities are conducted, many of which are breeding farms, i.e., cattle farming, piggeries, poultries, etc., and certain administrative regions are covered with cultivated plots, mostly energy crops (i.e., sunflowers, sugar beets), cereals (i.e., wheat, maize, barley, oats), cotton, potatoes, and hydroponic green houses. All the aforementioned crops are irrigated by river waterbodies, with pumping stations abstracting water from local aquifers and water collection basins via a carefully engineered complicated irrigation network. Topsoil fertilization threatens soft water quality through increased salinity and nitrate pollution. Furthermore, agents rich in nitrogen (N), via their fate in the soil and inevitable propagation in rock beds, cause ion mobility, mineralization, etc. Aquifers’ quality changes since, e.g., a new nitrogen pool enters the nitrogen cycle of the local ecosystem (Figure 1), unbalancing the water–soil–nutrient equilibrium. Yet, the humic part of the soil, microbiota, favors the formation of nitrous oxides, a strong greenhouse gas (GHG) with a great impact on climate change worldwide.

Water/pollutant flow through porous media demonstrates a high complexity embodied via mathematical simulation models. Complexity increases explainability to the detriment of the processing difficulties to be encountered. Ontologies describe in full detail well-defined interrelated phenomena, suitably bound in conceptual structures of fluids flowing through porous media which are applied in artificial intelligence and affect new infiltration model generation [10].

Nutrient leachate prediction models estimate not only the residual nitrate part applied on the cropland but also all potential seeping losses of the nitrate pool into varied soil profile layers, combined with local weather characteristics and farming practices. Artificial intelligence (AI) and machine learning models are gaining an even higher importance [11] as an alternate reliable method for handling complicated nonlinear hydrological modeling with good countrywide-scale predictions. In numerous cases, a lack of sufficient and proper data, necessary to attain hydrological model calibration, combined with many parameter inputs for demanding, profound modeling, drastically increases the processing burden and undermines prediction accuracy and reliability. Obstacles are overcome by using models based on AI and machine learning techniques presented in many publications, which reveal the future trends regarding surface and groundwater quality decision making [12,13,14,15].

The scope of this paper was to conduct a systematic review of leachate models useful for proactive and rehab actions to safeguard surface and subsurface soft water, which are becoming even more scarce. After intense literature research, it was concluded that the bibliography was lacking extensive research, incorporating leaching models for forecasting both surface and groundwater quality as an essential tool for integrated water source management.

Well-tested solute leaching models, standalone or as a part of an integral modeling package, provide rapid site-specific estimates of the leaching potential of chemical agents, mostly nitrates, below the root zone of crops and the impact of leaching towards groundwater. Most of the models examined were process-based or conceptual approaches. Nonetheless, empirical prediction models, though rather simplistic and therefore not preferable, demonstrate certain advantages since they do not require extensive calibration database information, which in many cases is unavailable, not to mention stochastic approaches and the involvement of AI.

2. Methodology

In order to isolate the suitable models adopted and agent fate methodology, publications were derived from Science Direct^®, Web of Science™ and Google Scholar scientific databases. Specific keywords, i.e., ‘model’, ‘nutrients’ fate’, ‘porous medium’, ‘infiltration’, ‘percolation’, ‘nitrogen leachate’, were tested, combined or stand-alone, to track down and compile the proper material, which was carefully scrutinized to extract the relevant cited content.

All findings were classified according to the emphasis drawn by the authors of the paper regarding the field of interest, though it was more or less expected that there would be a cognitive overlap. For instance, model packages are widely used to predict nutrient fate, and soil–water and soil–air balance, and thus the types of crops to be planted in the near future, as well as quantitative approaches to suitable fertilize use. A basic classification was made among nutrient, ion metal and other chemical agent leaching processes. The porous medium that stands as a hindrance to the pollutant flow justifies new reasons for further categorization. Temporal- and spatial-scale information, soil use, along with climatic data are of great importance for any assessment. All model packages incorporate significant components that are to be calibrated by time series data and previous relative research so as to obtain more reliable results. Components could be classified as physically based or conceptually distributed models, theoretical or mechanistic (i.e., process-based or conceptual), empirical, hybrid, machine learning, etc. The application of many model packages entails certain different dominant approaches governing each component. As regards the solute, simulating models predict either groundwater flow or solute transport, boundary transition zones, which employ numerical models with specific conditions, e.g., where salt intrusion in aquifers is to be monitored. Further categories are established based on the final prediction technique employed viz. finite difference against finite element techniques [16]. There have been cases where well-documented articles allowed ever deeper investigation by making use of their references to cover broadly and more completely topics of relevant interest. In other cases, hybrid models are hard to distinguish and classify. In such cases, the most profound characteristics determine the classification.

3. Materials and Methods

The majority of the models applied are mechanistic models (process-based), which satisfactorily describe dynamic processes and exploit accurate data used for model initialization. Empirical models rely on data correlations for the final outcome, while deterministic models make use of defined and well-established scientific laws in soil water and chemical agents’ dynamics to obtain the predictions. Stochastic models take into account variability and randomness concepts (input variables), providing a broader range of potential outcomes. Each type of model has its strengths/drawbacks and ideal use cases, depending on the specific research, the implementation scale area, or management accuracy and goals.

Mechanistic models are categorized as progressive conversion models where particle size remains unchanged during the leaching process without any penetration resistance to fluids/agents, a shrinking core model with constant particle size, a shrinking core model with shrinking particle size, etc. [17].

The way of approaching each case selected is to determine conceptual, empirical, physically based, hybrid models, steady (snapshot-like pictures) or dynamic (ongoing) simulation models. Another significant categorization depends on the extent of area appliance, i.e., pasture, cultivated plot, river catchment/basin, estuarine, coastal waters, aquifers, regional, countrywide, etc., and dimensional fate 1-D, 2-D, spatial analysis employed, e.g., distribution of lumped and huge heaps of data collected and tested from databases or models with minimum data requirements [18,19]. Groundwater modeling, when numerical models are employed, entails certain approaches, e.g., finite difference [20], finite volume [21], finite element, and element-free [22] methods.

Chemical agents, e.g., herbicides, complex ions, organic pollutant concentration, saline and fate, runoff, drainage, infiltration, percolation, seepage phenomena, etc., determine water quality deterioration, monitoring network, for integrated strategy and remedial actions. In complex soil layers, anion retention capacity varies, and surely soil nitrate flux does not correspond directly to the water soil infiltration flux and it is rather a function of the organic matter content. However, major categories located and analyzed in published papers of modeling are given below.

3.1. Process-Based or Conceptual Models

Process-based models employ diagrams and interlinks among parallel processing and flowcharts of mass transfer in between different zones (entities) to facilitate complex physical and biochemical interactions of soil, crops and water bodies [18]. Soil particle redox potential, electrical conductivity, etc., are ion transfer diffusion phenomena and leaching controllers [17].

Organic chemical screening is performed using leaching models, which account for the mobility of the chemicals in the soil. Despite not being able to forecast concentrations, they are still straightforward and only need information that can be found in reports from soil surveys and scientific publications. They can also be readily coupled with GIS to produce an effective evaluation tool for the control of non-point sources in agricultural watersheds [23,24].

Simple models with semi-empirical process descriptions of the lumped conceptual type which utilize time series of averaged accumulated water, e.g., on catchment level within predefined blocks [25], are presented next, such as ANSWERS [26], for watersheds where sub-catchments are divided into hydraulically interconnected elements (grids), a model structure approach known as ‘fully distributed’ that demands heaps of data and requires high computational burden, CREAMS [27,28], a field-scale model for chemical runoff and soil erosion, GLEAMS [29,30], developed to assess agricultural chemicals’ effects on water quality, SWRRB [31], a modified CREAMS, AGNPS [32] and AquiMod [33]. In such models, there has been a flux between segregated water body blocks following physical principles, i.e., surface flow, groundwater recharge, infiltration, percolation, subsurface flow, water table recharge, etc. [25].

Conceptually, leaching encompasses both the top layer of soil and the area beneath a plant’s roots depicting the soil-groundwater system. It could be considered that a soluble part of pesticide mass is instantly mobilized at the surface causing surface water infiltration into the rhizosphere.

In pastures, soil type contributes to 12% when referring to (N) leaching and a smaller contribution to (N₂) fixation. Still, soil profile and type remain the most significant factors involved in % (N) loss [34]. The agro-ecosystem model, EcoMod, with subsequent versions, was developed as a biophysical, pastoral simulation model [35]. Plants’ growth rate and carbon flux on the soil were simulated. Model modules regarding water and nutrient presence incorporate calculations for water and solute circulation, nutrients’ fate, leaching, adsorption, ammonium nitrification, gaseous (N₂) losses, and other geochemical phenomena, i.e., gradual immobilization, mineralization, etc. Fertilization and irrigation practices are included as well. Climate conditions were based upon data selected by means of stochastically created 99-year series climate documents by employing a modified version [36] of a daily climate model and incorporating data derived from the ‘Stochastic Climate Library’. By utilizing EcoMod, better regional management is applied via the feeding animal type for the pasture to be selected, i.e., cattle or sheep, and the adequate use of nitrogen-based fertilizers to be applied, for optimal results over sustaining the adequate pasture without all the negative leaching effects caused by nitrate pollution over the catchment of the zone of experimental interest (New Zealand). Nitrogen leaching appeared to be more intense during the winter. Furthermore, the application of nitrogen-based fertilizers, though increasing quantities of monthly nitrogen leaching and fate, still did not alter the pattern of % nitrogen loss, i.e., the cyclic pattern of nitrogen fixation [34].

A biogeochemical model based on denitrification–decomposition processing (DNDC) was developed by [37,38] for simulating dynamics of both carbon and nitrogen forms in soils for agro-ecosystems. DNDC simulates crop yield, carbon sequestration in soil, and nitrogen leaching when irrigated. Furthermore, it estimates greenhouse gas (GHG) emissions from terrestrial ecosystems and carbon sequestration [39,40]. A basic component of the model simulates crop growth and decomposition by processing data of soil conditions, i.e., moisture, redox potential, temperature, etc., and another component covers carbon and nitrogen transformation through aerobic nitrification, anoxic denitrification, and even anaerobic fermentation by means of biotic micro-population in soil. Furthermore, biogeochemical interactions are taken into consideration, and nitrogen is finally released into the atmosphere or even leaches in deeper soil sequestration after hydrological processing by means of nitrogen adsorption phenomena, plants’ uptake in the rhizosphere, microbial assimilation, nitrification/denitrification, etc. [41,42]. Zhang et al. (2021) [43] applied the DNDC biogeochemical model to quantify denitrification–decomposition bioprocessing as a mechanism and a part of overall nitrogen management of greenhouse vegetable fields in China. The model is developed for extrapolating prediction in extended time and carbon/nitrogen soil dynamics. As with the other process-based models, it requires time series data for a long period, usually over a decade, and long, intense calibration testing. However, cases of underestimation of measured N-NO₃ concentrations in soil leachate in certain parts of the year were recorded [43].

The DayCent model [44] simulated the nitrogen cycle in soils for various ecosystems, (e.g., cropland and forest). It simulates N₂O emissions and mineral nitrogen leaching under different types of landscapes, exploiting a variety of meteorological data, soil properties, irrigation practices, and crop particularities. More specifically, nitrogen leaching presents remarkable spatial and temporal variations, known as hot spots and hot moments (HSHM). Nitrogen leaching and loss within HSHM could be easily tracked and managed by means of applying the proper model to achieve suitable fertilizing management, local climate factors, soil profile properties and the local topography [45].

TETIS [46,47] is a process-based, hydrological, conceptual, distributed model that simulates aquifers’ recharge and soil nitrogen leaching, enabling the study of the long-term groundwater quantified response to nitrogen leaching. It incorporates precipitation data from meteorological time series, different irrigation and fertilization practices and potential evapotranspiration. The latter is obtained by means of the Hargreaves–Samani equation [48].

The nitrogen cycle is dependent on fertilization and atmospheric deposition. Corine land uses, maps, and ‘Pedotransfer’ functions were involved [47,49]. They were employed in combination with functions exploiting raw soil data upgraded into useful information tools via predictive functions of certain soil properties. Fifty years of meteorological data were combined with irrigation and fertilizing practices as well as the digital elevation model from the geographical survey of the site of interest. All selected data were the input of the TETIS model. Finally, the quantification and sensitivity of nitrogen recharge and nitrogen leaching corresponding to a variety of weather conditions were estimated on certain temporal bases in the Valencian region (location in Spain) [50].

STICS is a one-dimensional, daily-step, soil–crop dynamic model [51,52]. It simulates the quantities of daily drained water, (N) leaching in soil–water phases, (N) plant uptake and fixation, (N) fluxes, and dynamic interrelation between hybrid tested crops and soil type under various climatic parameters, e.g., air temperature, rainfall density, solar radiation, ‘Penman’ evapotranspiration, C:N ratio, pH, calcium carbonate equivalent action, etc., which finally affects crops’ biomass production [53]. Pedoclimatic characteristics (i.e., soil water content, nitrogen abundance in soil, bulk density, soil infiltration rate) and soil exploitation practices are used as initial inputs for the running of the simulation. Nitrate is transferred by convection mixing phenomena. A calibration stage is mandatory before the appliance of new cultivar parameters.

Grain legume-based cropping systems require a comprehensive reevaluation by taking advantage of bioprocesses, e.g., symbiotic biota for fixation and mitigation of leaching (N), nitrogen cycle cropping system reengineering, adopting crop succession, improved concepts as regards nitrogen-based fertilizer application, irrigation practices, and techniques. The solute transfer between subsoil profiles is conformed to the tipping bucket concept, i.e., downward mitigation after surpassing the soil’s profile water capacity and the prevention of aquifers’ nitrate pollution, focusing on soil nitrogen balance to avoid (N) leaching, in accordance with Direct. 91/676/EC concerning agricultural activities [53].

The model of standard version 9.2 of STICS [54] is a soil–crop model that computes changes in biomass and yield in soil organic carbon (carbon flux), predicts nitrate leaching, soil water and nitrogen fate, etc., by interpreting certain dependent variables and parameters, e.g., weather conditions, cropping practices [52], plant growth, carbon as (CO₂) and nitrogen fluxes [55], and solar radiation.

The latest version of STICS is based on monitoring the changes in the carbon pool as expressed by the gross primary productivity (GPP), dependent on autotrophic respiration, net primary productivity (NPP) via plants’ growth on a predefined time basis, and finally the complex component of Ecosystem Respiration (RECO), which is composed of autotrophic plant biomass, plant nitrogen, heterotrophic residual mineralization of the organic matter and net ecosystem exchange (NEE), which equals the summation of GPP and RECO. NEE represents the balance between carbon fixation via photosynthesis and respiration that releases it to the environment. Carbon flux variations are being recorded and underwent comparisons upon crop rotation. The model was implemented in Belgium for estimating CO₂ fluxes for rotating cropping, with its efficiency ranging from satisfactory to very good [55].

The AqYield model [56,57] is a simple dynamic model that requires only a few inputs (e.g., soil properties, daily climate features, dates of sowing, harvest, irrigation, tillage irrigation and soil tillage depth for crop management). The model estimates drainage sufficiently well, as well as water flows for several crops, major nitrogen flows in the soil, plant (N) uptake and mineralization. It estimates soil–water content dynamics, water drainage and evapotranspiration. It is tested and evaluated for the precision of the predictions accomplished. Although fairly simple, it is considered to be accurate in terms of (N) leachate prediction in crop rotation as much as other more sophisticated similar models, e.g., STICS. AqYield satisfactorily predicts (N) flows (fate) in the soil–plant system, including mineralization, plant uptake and mitigation on a daily basis. Cultivated crops, climatic data and soil characteristics have a great gravity in shaping the final predictions.

Great bibliographical research was conducted by Baveye (2023) [58] to emphasize the steps required for model development to predict soil carbon dynamics, interrelated to the nitrogen cycle, mostly derived from fertilizers. According to his argument, current ecosystem-scale models are introducing limitations when applied to ecosystems due to a lack of the proper interdisciplinarity and “bottom-up” approach, making use of the microscale soil processes. Furthermore, interesting for stipulating empirical models and applicable at large spatial scales, it is still valuable when upscaling efforts. Thus, modelists should stay focused on the micro-scale of soil microorganisms at first and progressively try to move up regarding the spatial scale, incorporating characteristics of the region of interest. Already known or future empirical models are providing valuable services for the final upscaling target.

Topsoil carbon undergoes various transformations mainly as dissolved organic carbon (DOC) and particulate organic carbon (POC). The latter has a vivid role in numerous flocculation and adsorption phenomena affecting soil physicochemical properties. DOC represents the soluble organic part and holds a crucial role in soil transformation via microorganisms’ uptake availability, the high soil mobility/leaching, biochemical transformation by means of metal ion/organic chemical binding and toxicity phenomena through biosorption. Ref. [59] developed and introduced a modified TRIPLEX-DOC model focused on leaching, sorption, DOC and biodegradation phenomena [60] to simulate DOC dynamics in monsoon forest ecosystems since it does not incorporate itself as a component simulating responses of DOC concentrations and fluxes to the atmospheric N deposition. By means of TRIPLEX-DOC model improvements, a more profound biogeochemical model was incorporated to predict more accurately DOC fluxes in forest ecosystems in the monsoon regions which differentiate them in terms of vegetation and NPP. Furthermore, the modified model predicts more accurately regional carbon cycle in seasonal patterns and assesses more safely soil DOC fluxes in local ecosystems.

Nitrate leaching occurs in croplands where synthetic and animal biowaste-nitrogen-based fertilizers are applied, which affect vulnerable aquifers (e.g., karsts) from nitrate pollution. The soil and water assessment tool (SWAT) [61], developed by the US Department of Agriculture (USDA) and agricultural research service (ARS), is widely exploited to simulate the hydrological cycle, plant growth, and chemical leaching in numerous watersheds and cultivated soils. SWAT (CATCH) is a distributed, semi-empirical [62], physically based hydrologic model (DPBHM), which incorporates the variable storage coefficient (VSC) method. The latter is a kinematic wave method, which means that the streamflow equation is simplified by assuming that the friction slope is approximately equal to the slope of the, e.g., watershed channel. The proper use of SWAT simulation corrects the initial assessment of certain indices, e.g., dendritic connectivity index (DCI), a measure of longitudinal connectivity of aquatic ecosystem status, which outlines that the temporal resolution of river water routing (time steps) plays a dominant role in the final assessments. It is noteworthy that time steps are dependent on actual watershed size and configuration [63]. SWAT employs the vegetative filter strip MODel (VFSMOD), which is an empirical model [64] that calculates sediment reduction. It simulates crop yields and nitrate leaching under a variety of nutrient and irrigation management practices as a well-tested prediction tool to improve management practices upon safeguarding high groundwater quality towards agricultural sustainability. SWAT is combined easily with sequential uncertainty fitting (SUFI-2), uncertainty procedures (SWAT-CUP 2012), and the Nash–Sutcliffe model efficiency (NSE) validation test [65].

SWAT is modified by coupling with shuffled frog leaping algorithms and a farm-level economic model and cost estimator (FEM). The model outcome (MOSFLA) demonstrates powerful convergence and optimization ability [66].

The SWAT tool predicts and quantifies nitrate leaching pathways and prevents groundwater nitrate pollution, which threatens drinking water resources and unbalances ecosystems. Nitrate pollution assessment changes fertilizing practices, alters the crops and prioritizes new sustainable agricultural methodologies and management practices in agribusiness. The crucial nitrate pollution drivers are the type of the soil, climate variability, crops irrigation, and fertilization practices over cropland [65].

The coupled SWAT (version 2012/Rev664) and MODFLOW models [67,68,69] perform better during complex surface–groundwater interaction analysis and explicit modeling of the groundwater system and surface water [65], in comparison with field-scale cropping system models such as decision support system for agrotechnology transfer (DSSAT) [70], HYDRUS 1-D [71,72], root zone water quality model (RZWQM) [73,74] and leaching estimation and chemistry model (LEACHM) [75]. All the aforementioned cannot accept as a complementary component a hydrologic model so as to drive to better predictions.

Modified croplands and watershed SWAT model coupled with the groundwater model and stream–aquifer interaction hydrologic MODFLOW compose the improved SWATMOD model [76], which demonstrates simulation capability of surface water, stream–aquifer interactions and groundwater [16].

The HYDRUS-1D model was employed and calibrated before use against nitrate concentration in soil water across all soil layers and the measured soil moisture. It was validated independently and finally started to simulate N-NO₃ leaching under certain conditions, e.g., controlled fertilization rate within prearranged irrigation depth or vice versa, i.e., regulated irrigation depth combined with a steady fertilization rate. Concurrently, it was assumed that there were different shifts in water table depth. Experimental site-specific soil physical and hydraulic properties were selected as well as data from an automated meteorological station, i.e., net radiation (Rn), barometric pressure (BP), temperature (T), wind speed (W), relative humidity (RH) and precipitation at 60 min intervals [72]. It is commonly employed in landfill hydrological evaluation [77].

The Penman–Monteith equation was utilized in conjunction with the meteo data obtained to determine the reference evapotranspiration [72]. HYDRUS-1D employs Richards’ equation [78] to simulate the unsaturated water flow [79]. The mass balance of nitrification—first-order reaction rate constants—and denitrification along with N-NH₄⁺ volatilization rate was taken into consideration. The soil–water characteristics curve was depicted by using the van Genuchten–Mualem equation [80] and the pedotransfer function model [49,72] coefficients and parameters related to the hydraulic transport and transformation (see Figure 2). Solute transport in heterogeneous waste rocks could be simulated by HYDRUS-1D since it supports multiple porosity components [81].

Dynamic leaching flux and soil water storage including dissolved CO₂ and N₂O conc. can be simulated with good results by implementing the HYDRUS-3D finite element model [82,83]. It entails domain, finite element mesh, defined boundary conditions and the input of topsoil vertical layers based on Digital Elevation Model (DEM) surface and topsoil thickness information. It estimates soil and bedrock hydraulic properties including CO₂ and N₂O storage, along with their leaching flow rate. Application of HYDRUS-3D over topsoil reveals the critical influencing, leaching factors (i.e., temperature, fertilizing, precipitations) of diluted CO₂ and N₂O (the latter a strong GHG) in water and thus promotes the deeper understanding of the nitrogen cycle mechanism in terrestrial ecosystems [83].

Efforts were made to estimate (N) leaching quantification of irrigated maize by testing different fertilizers, regulating, through pumping and irrigation, the water table and adopting improved irrigation management practices. During these efforts, conventional fertilization practices were tested as a reference scenario and a field experimental trial was conducted for consecutive years. Subsoil zones were identified in which the leaching fluctuates within a hydrologic year [72].

Land use investigation combined with climate change was analyzed by implementing a global vegetation model (LPJ-GUESS) [84]. A trade-off between crop yield and nitrogen soil leaching was drawn in certain scenarios of an increase in wheat and maize yield for various regions. The integrated assessment model MESSAGE was employed to simulate fertilizing appliances, making use of drivers such as representative concentration pathways 8.5 [85]. The distribution of nitrogen application rate information was derived by using the (LPJ-GUESS) model after being fed with data selected from the Common Agricultural Policy Regionalized Impact (CAPRI) model at a terrain grid level up to 1 km². Climate and land use change projection assess nitrogen leaching, CO₂ mitigation and crop yield [86].

A new approach of monitoring nitrate leaching of land fertilization is obtained by the NIT-DRAIN model [87]. It simulates nitrate conc. at a subsurface drainage network’s outflow. It is a drainage discharge simulation model instead of a monitoring/observation model. Water and soluble nitrates are transferred through the soil profile, which is separated into three successive, interconnected, subsurface stratifications, segregated by drain and mid-drain layers. Thus, there is a distinguishable water–nitrate fast transfer throughout the macro-porous upper layer, located above the pipe network. Low and residual nitrate transfers are accomplished through the lower conceptual soil stratifications. The nitrogen load to the ground is divided into two discrete phases. First is the seasonal applied nitrogen quantity, which entails all predicted nitrogen transformations at the cropland scale, and second is the remaining off-seasonal nitrogen pool, which undergoes extended leaching phenomena when the winter season starts. Both prediction data are required. The model also requires updated variable input at the commencement of a new hydrological cycle. It involves seven nitrate leaching and water flow parameters and employs two different transfer functions as long as nitrogen fate lasts. Model calibration is based on Generalized Reduced Gradient (GRG), a non-linear regression algorithm and the hierarchical scheme for validation by making use of the split-sample test [88].

GOSSYM is a mass balance mechanistic two-dimensional (2D) gridded soil model that simulates water, carbon and nitrogen interactions in soil, plant root zone and crop response to climate variables and water irrigation. It incorporates many routines as components, such as daily weather information, soil profile characteristics and parameters, plant growth data, etc. Modification is presented by coupling the 2DSOIL mechanistic 2D finite element soil process model. The latter simulates underground processes, i.e., mineralization, organic matter immobilization, nitrification and denitrification [89]. The modified GOSSYM simulates a variety of potential climate scenarios encountered and facilitates decision and policymakers as regards sustainable strategies. GOSSYM is also to be used coupled with the COMAX expert system developed ad hoc. The inference engine incorporated is very useful for cultivation practices, model result interpretation and irrigation and fertilizing regulation [18,90]. GOSSYM-COMAX is widely validated by being tested under different environmental conditions and crop practices.

The new climate regime over certain regions in Europe incurs even more extreme rainfall incidents with catastrophic ecological results. The abstraction of the humic topsoil tends to be a severe negative outcome. Therefore, it is of crucial importance to use integrated biogeochemical–ecosystem models and estimate intra-/inter-annual gross primary productivity (GPP) variations, e.g., Biome-BGC [91,92,93], to monitor ecosystem response against extreme events. Interactions of ten hydrological and ecological processes were taken into consideration, including runoff, canopy evaporation, soil–water storage, soil evaporation/respiration, transpiration, net primary productivity (NPP), net ecosystem exchange, nitrogen mineralization and leaching. Once more, nitrogen propagation incurs nitrate pollution and is considered to be of high-priority concern when the Good Environmental Status (GES) or even the Good Ecological Status is to be assessed. The model focuses on carbon (C) and nitrogen (N) fluxes on a preset time scale (i.e., daily, monthly, annual). Model parameterization is achieved by making use of site characteristics data (e.g., soil texture/relief/depth, terrain elevation), meteorological data (e.g., precipitation, humidity, temperature, etc.), and eco-parameters (e.g. canopy growth and expansion, photosynthetic rate, carbon to nitrogen ratio of leafage, lignin fraction of the dead wood) [94].

As regards the part of the daily soil–water balance, the one-dimensional soil–plant–atmosphere DAISY, Danish model simulation (version 4.01) [95] was employed to cover the water and nitrogen balance in agro-ecosystems for crop cultivation [96]. The model comprises three main modules, i.e., a bioclimate, vegetation, and a soil component. Soil–water retention and transport were simulated by employing the DAISY model and using the Makkink equation, while evapotranspiration was determined from the daily global radiation and mean temperature [97]. Variables for nitrate leaching, i.e., nitrate percolation, entail crop classification into groups according to (N) uptake performance, residual (N), contribution to leachate and (N) mineralization, i.e., transformation into inorganic form (NH₄⁺) [98].

Nitrate leaching predictions and nitrogen conc. in monitoring sites in Denmark, including various parameters, i.e., soil type, climatic data, crop consequence, nitrogen fertilizer appliance rate, soil winter capping, etc., were conducted, making use of multivariable experiments. A linear regression was applied to identify and assess the influence of gravity of a leaching year (hydrological year). A certain number of sites were selected and the DAISY model (ver. 4.01) [95] (Figure 3) was implemented to simulate water percolation and balance at the depth of the rhizosphere. Each DAISY module processes individual fields based on well-tested and widely accepted scientific experience. All modules require a heap of time series datasets, which are not always easy to obtain, and verification. Soil stratification forms individual modules with domain equations, e.g., the Mualem-van Genuchten eq., which describes water retention curves and soil hydraulic conductivity, a critical parameter for solid prediction or soil water flux by making use of Richards’ equations. Module results are interchangeable between different processing fields for the optimized final outcome. The DAISY model is employed for quantitative description of water flow into an unsaturated soil zone and makes use of certain soil quality characteristics, i.e., water retention, unsaturated hydraulic conductivity, which were fitted earlier to the Mualem-van Genuchten equations [80,99] and RETC optimization computer programming code [100]. In the specific case, the DAISY model simulates the water balance regarding different soil–crop productions. The model incorporates Richard’s equation [78] to calculate soil water flux. Different soil sites and differentiated climatic data help deduce new estimated values of nitrate leaching; therefore, proper cropping strategies should be followed for soil nutrient balancing [101].

‘MIKE SHE’ is a complex model package which describes distributed and physically based water/solute flow in catchment areas. It incorporates the snowmelt process along with evapotranspiration and gives numerical solutions for overland (2D), unsaturated flow (1D), channel flow (1D) and saturated flow (3D). The combination of ‘Daisy’ and ‘MIKE SHE’ models enables water and nitrate simulation transport and overland flow on a catchment level, excluding intense rainfall events, i.e., Hortonian incidents [102].

Strict cropland’s nitrogen-based fertilization regulations in (kg N ha⁻¹) in Europe compel farmers to resort to alternative cultivating options, i.e., catch crops, to regulate post-harvesting nitrogen concentration of soil–rhizosphere nutrient balance. Some cultivations were tested over time, e.g., winter rye, spring barley, fodder radish, to achieve lower nitrogen leaching results. Simulation of the cultivation change during winter and spring, by using the biophysical agricultural production system simulator (APSIM) simulation model [103] (Figure 4), is parameterized over the mineralization of catch crops. Nitrate leaching was based on weighed percolation drainage within periods of interest. APSIM comprises certain modules, i.e., SurfaceOM, SoilN, SoilWat, canopy model and cultivar plant type. Each one of the modules simulates different fields of interest, e.g., water movement, N and C soil dynamics, plants’ solar radiation competition, etc. SoilWat is a module of APSIM. It has been developed as a cascading water balance model in which, on a daily basis, water balance is estimated by simulating runoff, saturated/unsaturated water flow, solute ground and underground movement interrelated with saturated/unsaturated flow, plant transpiration and soil evaporation. The soil nitrogen module simulates nitrification, denitrification, urea hydrolysis, and nitrogen mineralization [104]. Nitrogen originated mainly by manure application over cropland and inorganic-based fertilizers [105].

APSIM’s appliance entity (i.e., plant–rhizosphere–soil–atmosphere) functions on a daily time frame [103]. The prediction ensures reliable crop management strategies, all year long, for the sake of a balanced ecosystem, minimizing all negative environmental impacts as regards crop yield, water, nitrogen, and carbon mitigation dynamics [105]. Moreover, this model has been developed for sugarcane simulations, tested and confirmed at the paddock scale, since it incorporates modules for specific crops [106,107]. Thus, it simulates management practices, water uptake and growth of sugarcane [104].

Intermediate percolation calculations are conducted by using the model EVACROP v.3.0, updated from EVACROP v.1.5 [108,109]. Nitrogen leaching affects water quality and soil acidification. A bio-geophysical, process-based, multi-component ecosystem model (CoupModel) [110] was employed to estimate carbon and nitrogen fluxes, water and heat balance in the eco-terrestrial cycle. It facilitates the assessment of the local ecosystem (N) balance, e.g., manure application overtillage serving as biofertilizer. Nitrogen transformation includes (N) plant uptake and mineralization. It runs on a daily time frame and on a minimal square meter unit grid. Model running requires certain parameters, i.e., weather (precipitation) data, solar radiation, temperature, relative humidity, wind speed, precipitation and dry deposition as regards (N) information.

Carbon and nitrogen storage incorporates abiotic/inorganic, i.e., ammonium and nitrates in the soil, and biotic part, e.g., plant tissues and external characteristics such as leaf area and solar radiation exposure, which regulate carbon assimilation. The model regards the soil part as a series of constituent, interrelated layers where water, heat, nitrogen and carbon interact in a dynamic way. Darcy’s law and the generalized Richards (1931) equations [100] for unsaturated conditions govern soil water flux.

Soil evaporation phenomena were calculated by using the Penman–Monteith equation [111]. Outflows of the groundwater table are determined by a linear empirical drainage function. Soluble organic matter (SOM), (N) mineralization and plants’ water uptake are dependent on moisture and soil temperature. Other dissolved forms of (C) and (N) comprise nutrient pools in the roots. Microbial biomass of the seeded roots (mycorrhiza) regulates stoichiometry of C/N ration and carbon use efficiency (CUE). Any changes in the nitrifying biomass of a specific soil layer affect eminently the soil nitrification flux and therefore the nitrification rate and the soil–water–ammonium conc., since dissolved organic nitrogen (DON) and ammonium (N-NH₄) are in chemical equilibrium in both the soil–water and soil–solid phases [112].

The Nitrogen Loss and Environmental Assessment Package (NLEAP) is a powerful mechanistic model that provides rapid site-specific estimates of N-NO₃ leaching potential below the root zone of crops and the impact of nitrate leaching into groundwater [113]. Under various combinations of soil profile characteristics, weather data, and farming practices, the aforementioned model is used to estimate the residual nitrates and potential nitrate leaching losses from cropland soils into subsurface layers [114]. It runs in three temporal modes, i.e., annual, monthly and event-by-event for certain water–nitrogen cases and potential leaching.

The updated and improved NLEAP-GIS (version 4.2), coupled with geographic information system (GIS) spatial soil database as a complementary component, increases the capability of assessing (N) losses towards risky landscapes and combinations of different cropping systems and evaluates more accurately management practices over nitrogen transformation and mitigation. Testing over the north China plains, cultivated in seasonal rotation with wheat and maize crops, combined with meta-analysis by exploiting relevant literature, showed remarkable reliability [115,116].

The updated version of the model includes infiltration and transport of nitrates and soil water; carbon and nitrogen terrestrial cycle; soil surface and soil profile propagation and transformations; water, nitrate/ammonium surface runoff; nitrate leaching from the root zone and ammonium uptake from the seeded plants; denitrification losses and ammonia volatilization. Each individual process is prescribed by detailed algorithms and equations [116].

Model inputs such as daily meteorological data, including maximum and minimum temperatures, daily rainfall, relative humidity and evaporation are prerequisites to running various scenarios enriched with soil profile information and fertilizing events. During the winter wheat and summer maize season, a specific (N) application rate is recommended so as to be achievable; concurrently, higher (N) use efficiency and grain yield result in lower groundwater nitrate pollution risk. Nitrate leaching indicates the presence of a nitrogen pool which might affect local aquifers, identifying regional soil profile characteristics. The model’s outcome is validated by using older measured nitrate leaching reports. Results in many cases are comparable with other models’ outcomes, e.g., the DNDC model [117], on a regional scale [118].

In the large-scale and spatial variation simulation of nitrate leaching in the region of experimental interest (location in China), the rate of fertilizer N application was positively correlated with rainfall density; however, it was negatively correlated with N use efficiency [119].

Climate change and the interrelation of anthropogenic pressure on waterbodies’ catchments and basins are of great importance. Therefore, the evaluation and simulation of water resource management scenarios for adopted, resilient plans over coastal agricultural watersheds were conducted. It was achieved by the implementation of an integrated modeling system (IMS) that was set up to cope with the complexity of croplands in the vicinity of estuarine in the Med zone [120]. IMS incorporates certain components of reservoir operation (UTHRL) [121,122], surface hydrology (UTHBAL), called (R-UTHBAL) built in R statistical language [123], groundwater hydrology (MODFLOW) [67], crop growth/nitrate leaching (REPIC), which is a coupled Environmental Policy Integrated Climate (EPIC) [124,125] model with R-ArcGIS bridge application (ESRI), nitrate pollution flow, multi-species, transport model for simulation of dispersion, advection and chemical reactions of contaminants in groundwater systems (MT3DMS) [126] and the prediction model for seawater intrusion cases (SEAWAT) [127].

When it comes to groundwater dynamics, aquifer interactions with the stream system, surface water and nutrient fluxes at the watershed outlet, and water and nutrient leaching from the surface to the aquifer, the Integrated Surface and Subsurface Model (ISSM) [128] produces good prediction results. It consists of the in-stream water quality model (QUAL2E), the groundwater models MODFLOW and MT3DMS, and the hydrological model SWAT.

PATRICAL is a conceptual large-scale (area grid 1 × 1 km²) temporal and spatial distribution model, addressing water quality and balance with remarkable time projection prediction. It enables an overall perspective of nitrate pollution in extensive regions and facilitates countermeasures for aquifers and wetland recovery to meet EU WFD requirements. It entails calibration, validation and future scenarios. When groundwater bodies are considered, it incorporates tens of lumped models [129,130].

3.2. Empirical Models or Statistical Models

There have been cases where conventional models are considered inefficient when the case is soils with cracks and high heterogeneity in terms of soil texture, particle shape and orientation, burrows, etc. Thus, the diffusion coefficient is difficult to adopt for extensive tortuosity. In such cases, many experimental data are needed or suitable empirical correlations must be employed [17]. Empirical models demonstrate simplistic concepts and are, in some cases, e.g., in regions that lack time series data, more attractive since they are easy to use and they do not necessitate profound experience in soil science and hydrological modeling. Empirical models might be simple equations with region-specific parameters [58]. They exploit collected datasets and allow prompt result acquisition and quicker final assessment and therefore prompt decision making. Calibration is less demanding, relying on observational data. On the other hand, empirical model prediction ability is fairly limited with narrow scenario flexibility and, in general, lacks accuracy and suffers quite often from oversimplification. It is apparent that in complex hydrological processes, significant soil–water interaction mechanisms are overlooked, a fact that is functioning as a deterrent to their adoption and usage.

The HELP model is a hybrid model, both deterministic and statistical–empirical, that simulates water vertical flow through landfill layers. It proved to be quite useful as regards landfill capping water balance systems and leachate generation in northern Germany (see also Section 4.4).

Nonetheless, empirical models are lacking satisfactory results when extrapolation is needed in the future. Despite this, it is still a useful tool in the decision making in farming or grazing [18]. The NLES5 model [98] is partially modified based on an earlier NLES4 model version [131] since it has almost the same structure and partially shares datasets for calibration. It is considered to be an empirical prediction model for quantifying nitrate leaching on an annual basis, considering the interest zone as the root zone, i.e., 1 m depth. The model accounts for incurred effects of added N under certain crop sequences, seasonal crop cover, topsoil types, and local weather conditions. Soil (N) leaching and mitigation prediction, caused by fertilizing over croplands, improved integrated water basin management, and promoted the good quality preservation of surface water and aquifers as the main goals of model development.

The Quick Plant RZWQM2 sub-model is a simplified empirical plant module developed to simulate the water and nitrate fate for the crops and therefore to compute on a daily basis water and nitrogen uptake of the cultivated soil (see also Section 4.2 below). Meteorological data collection is essential to the final outcome. It incorporates the Green-Ampt infiltration equation, Richards’ equation [78] for water redistribution, and a plethora of submodules such as Quick Plant, soil water and heat transfer, N balance, generic plant growth, evapotranspiration (PET), soil equilibrium chemistry, pesticides and finally the management module. Soil water retention curves are acquired by using the modified Brooks–Corey equation.

Empirical prediction models demonstrate certain advantages since they do not require extensive calibration database information, which in many cases is unavailable [132]. Any future strategy must address the critical issue of relatively accurate nitrate leaching prediction across common cropping systems, soil types, and climate conditions in specific geographic areas, as well as the impact of seasonal vegetation characteristics on nitrate leaching, which is dependent on N fertilization practices. A carefully defined exponential function was fitted to the selected data. The function incorporated parameters that were estimated by non-linear regression analysis. The prompted leaching curve yields the marginal nitrate leaching rate, which corresponds to the recommended N application rate.

For the prediction of soil bulk density after tillage, an empirical equation was used in the water erosion prediction project (WEPP) model. The equation is based on the (EPIC) model [124,133]. The vegetative filter strip model (VFSMOD) as a coupled component of the SWAT model (see also Section 3.1) is also an empirical model that calculates sediment reduction [64].

3.3. Deterministic Models

The deterministic models are classified into static—time is not considered a variable—and dynamic models [18]. A further subclassification is lumped or distributed models [134]. DRAINMOD is a deterministic hydrological model employed for agricultural subsurface drainage for nutrient transport and groundwater salinity problems. Variants of the model are applied for nitrogen subsoil fate DRAINMOD-NII, salinity penetration in soil cropping DRAINMOD-S and phosphorus (P) concentration prediction and dynamic DRAINMOD-P [16,19,135,136,137,138]. The model is well tested over a river basin in Belgium for nitrate pollution prediction [139]. Nonetheless, certain limitations have been reported when implemented in artificially drained lands.

MIKE-11 is a 1-D hydrodynamic model in rivers that simulates dynamic water movement in channels and rivers. It has been applied as a water quality model in England and India. It employs time series of depth, pollutants, and flow data along with water quality parameters [140].

The artificial neural network (ANN) science field combines bidirectional long short-term memory (BiLSTM) and adaptive neurofuzzy inference system (ANFIS) to predict water quality in different groundwaters by employing single exponential smoothing (SES) as a preprocessing method to adjust the weight of the dataset input (categorized as training and testing data) [141]. The internal operations of a neural network are deterministic, not stochastic, after training is finished.

3.4. Stochastic Models

When data are presented using stochastic modeling, specific degrees of randomness or unpredictability are taken into account when predicting results. Using random variables, it predicts the likelihood of different outcomes under various scenarios.

SIMCAT it is considered to be a model based on a deterministic, stochastic, and Monte Carlo approach. It is used for the prediction of various biochemical indices and ion leachate, i.e., BOD, DO, and Cl⁻, NH₄⁺ NO₃⁻ [19,142].

Monte Carlo, a specific branch of stochastic modeling, is a broad class of computational techniques that rely on periodic random sampling to obtain numerical results. It uses randomness to solve problems that might be deterministic in principle [143].

Vadose zone flow and transport model (VADOFT) is a 1-D finite-element prediction code applied to chemical transport, flow/fate in the unsaturated zone. It employs parameters such as pressure, water content, and hydraulic conductivity to solve the flow equations. The code, when equipped with a Monte Carlo pre- and post-processor, enables the running of multi-parameter scenarios several hundred times and provides stochastic (probabilistic) outputs [144].

3.5. Artificial Intelligence and Machine Learning Models

Artificial intelligence (AI) has become involved in recent years with forecasting groundwater quality modeling methods, e.g., artificial neural network (ANN), evolutionary algorithm (EA), etc. Given its capacity to handle enormous volumes of data, it offers an alternate method for handling complicated nonlinear hydrological modeling [145,146]. The proper water quality parameter selection is from every aspect crucial in order to attain suitable AI model training. In every strategy, actual, in situ datasets are to be directly compared with those of AI method testing [147]. AI is advantageous over non-AI models by reducing the time spent for data sampling and AI proneness to rapid nonlinearity identification patterns as regards input and output data [12].

AI models combined with metaheuristic optimization techniques demonstrate higher reliability in terms of capturing the nonlinearity of water quality parameters [147]. General categorizations of AI methodology for soft water quality estimation include ANN modeling, fuzzy logic (FL)-based models, support vector machine (SVM) models, machine learning (ML) and hybrid models.

A machine learning (ML) model utilizes potentially either deterministic or stochastic methods in different sectors to obtain the proper results via prediction methodology. ML models, such as adaptive neuro-fuzzy inference system (ANFIS), deep learning (DL) [148], evolutionary computing (EC), ensemble learning (EL), hybrid modeling (HM) or even support vector machine (SVM), support vector regression (SVR), were introduced and developed for the water quality parameter prediction and thus groundwater quality classification for irrigation purposes [11,12,147,148,149,150]. ML models rapidly improve groundwater level forecasting, which is regarded as critical for any water management planning [13].

ANN exploits relationships between input and output datasets [147], and is produced via neurons, a computational model that excels at content addressable memory, machine learning, pattern recognition and optimization [151,152]. ANN uses several algorithms, such as back-propagation neural network (BPNN), Levenberg–Marquardt back-propagation (LMBP) [12,13], feedforward neural networks (FFNNs), subcategorized into single layer perceptron (SLP) and multi-layer perceptron (MLP) [147]. They are preferrable for predicting spatial distribution parameters in aquifer remediation [12]. ANN modeling was applied in numerous cases over various regions, e.g., in India [153,154], for groundwater quality prediction. Deep neural network (DNN) within ANN modeling enables accurate estimates of nitrates and heavy metals, i.e., cadmium and chromium [155].

Because of their quicker optimization and capability for generalization, EA and SVM demonstrate higher predictive performance comparable with ANN and ANFIS [156,157], albeit limited studies were completed regarding groundwater quality forecasting so as to enhance confidence about the proper effectiveness for complex hydrogeological system simulation. A major drawback is considered to be the long training time. Nonetheless, in the near future, the ANN methodology shall be improved, and the ANFIS technique, which combines ANN and fuzzy inference system advantages, shall play a major role. Furthermore, ANNs, e.g., back-propagation neural network (BPNN), Levenberg–Marquardt back-propagation (LMBP), and MLP algorithms, are the most preferable in AI groundwater modeling due to their accuracy [12]. ML models, in many cases, analyze landfill leachate quantity/quality. Thus, e.g., a hybrid artificial intelligence model (AIM) based on a grey wolf metaheuristic optimization algorithm and a two-stage extreme learning machine (ELM-GWO) is adopted to predict landfill leachate quality parameters in Iran. Other single-stage AIMs can be mentioned (MARS, MLPANN, ELM, etc.), as well as two-stage AIMs (MLPANN-GWO and ELMGWO, etc.) [14].

FL-based models make use of adaptive neurofuzzy inference systems (ANFIS), which is an integration of fuzzy inference systems (FIS) and adaptive neural networks. Hanoon et al. (2021) [147] and Haggerty et al. (2023) [148] presented analytical tables of AI models and adopted learning methods to support groundwater quality forecast. Ensemble fuzzy models combine fuzzy logic methods with ensemble learning for better performance outcomes. They have been applied exclusively to improving DRASTIC method performance [148,158].

Recurrent neural networks (RNNs), integrated with geographic information system (GIS) technology, enable scientists to accurately predict groundwater quality indices and cope with health risk management [159]. A detailed depiction of aforementioned AI techniques is summarized in Figure 5.

3.6. Physics-Based Models

Physics-based models are mostly one-dimensional leaching models, i.e., RZWQM [160,161], WAVE [162,163,164] and DAISY [165], which simulate root zone processing. Numerous models are hybrid, i.e., process- and physics-based models, e.g., MODFLOW/MODFLOW-MT3D (see Section 3.1).

Daisy simulated crop production and nitrogen and water balance in the root zone [102]. It includes modules and soil–water dynamics based on Richards’ equation [78]. It incorporates nitrogen transformation, i.e., mineralization/immobilization, nitrification, denitrification and agricultural management practices.

Numerous RZWQM components were developed to improve simulation accuracy regarding crop root zone. Therefore, RZWQM contains a soil water and heat transfer module [166,167], a generic plant growth module [168], a nitrogen balance module [169], a soil equilibrium chemistry module [170], an evapotranspiration (PET) module [171], a management module [172] and a pesticide module [173].

The modeling system MIKE SHE describes the distribution of solutes and water flow in a catchment using physical principles. This entails the numerical solutions of the coupled partial differential equations for the processes of evapotranspiration and snowmelt for overland (2-D), channel (1-D), unsaturated (1-D), and saturated (3-D) flow. A full modeling system for simulating the movement of water and nitrate within a watershed can be created by integrating Daisy with MIKE SHE [102].

Phosphorus (P) is an important nutrient and, though less abundant in surface water compared to nitrogen, is still within a constant proportion, N:P, e.g., 14.7:1 in the sea column [174]. Ratio unbalancing brings about eutrophication phenomena in aquatic ecosystems [175]. Therefore, the study of phosphorus fate mechanisms and selective infiltration routes in terrestrial and aquatic ecosystems is of high priority. Pferdmenges et al. (2020) [176] introduced a comprehensive review of phosphorus–soil interaction models, classified into multiple categories, such as temporal and spatial scale, surface/subsurface transport, matrix/macropore transport and mobile/immobile transition in dual-porosity models.

4. Metal Ion Leaching and Solute Transport

4.1. Soil Medium

The geochemical PHREEQC code [177] performs sufficient numerical simulations incorporating mixing transport models both in the aqueous and gaseous phases, taking into account geochemical reactions such as precipitation, dissolution, complexation phenomena involving metal oxides and microbial activity. The reactive transport model incorporates reaction kinetics for chemical processes, including ion association and specific ion interaction theory for solute activity calculations [176]. In a publication, it was employed to calculate saturation indices (SIs) [178]. The simulation code was subsidized by predicting/estimating tools for model parameters, such as parameter estimation (PEST) software (version 5.0) [179]. Sorption phenomena are simulated by employing a two-layer model introduced by [180]. Organic matter sorption was modeled by implementing the WHAM model, an acronym of Windermere humic aqueous model [181], which is based upon humic acid behavior according to Lewis’ theory for electrondonors. Mine tailings and heavy metal leaching, e.g., Pb, were encountered by activating reclamation measurements to mitigate negative leaching effects. Mining slurry combined with manure leads to metal sorption, reducing any leaching processing. A new biogeochemical model was developed taking into account certain phenomena, i.e., kinetically controlled dissolution/precipitation, adsorption, water gas exchanges, surface complexation reactions, microbial respiration and growth, dissolution and precipitation. The amended model more accurately predicts Pb reactivity and soil tailings [182].

Heavily contaminated soils (brownfield) by potentially toxic elements (PTEs) are a permanent threat to the local ecology via toxicity and bioaccumulation. Human wellbeing is put in peril by leaching and runoff phenomena. Threats are growing even bigger considering the pH change in the soil cap. Therefore, chemically burdened sites have to be under constant monitoring in terms of heavy metal quantification and ion mobility checking indices to ensure that surface watersheds and aquifers are not threatened. It is acknowledged that there is a lack of detailed knowledge of minerals which exert control over toxic element leaching. Thus, it is of great importance to investigate soil mineralogy in PTE release and predict leaching [183]. The geochemical modeling program PHREEQC (version 3.1) was deployed to calculate SIs, which indicate whether a specific mineral is likely to dissolve or precipitate in groundwater, in a case study in Pakistan of monitoring groundwater areas suffering from arsenic contamination [178]. Geochemical simulations were conducted making use of PHREEQC software (version 3) [177], MINTEQ’s two thermodynamic databases [184] and Lawrence Livermore national laboratory (LLNL).

Sampling investigations conducted at a brownfield site served for fertilizer production. Jarosite rich in Pb, hematite, and gypsum were the most abundant mineralogical phases/stratifications, with zinc sulfate, kintoreite, and anglesite. Pb and Zn phases were identified as the dominant ones [183]. pH-dependent leaching tests were applied incl. HNO₃ and NaOH as the pH control agents in combination with geochemical models. The testing target was the reveal of leaching mechanisms and contaminant solubility in a pH ranging from 1 to 12. All information gained advances scientific knowledge, facilitates future remediation strategies, and promotes integrated sustainable management and strategy design over brownfields [183].

Barren piles of mining undergo bio-oxidation, giving rise to metal sulfide oxidation and finally acidification phenomena that motivate ion mobility, well known in the scientific community as acid mine drainage (AMD). AMD leachate mitigation exerts great pressure on bedrock, surface waters, and local aquifers since metal ions’ active plume puts at risk the overall ecological quality of the region in the vicinity of the mines.

Biogeochemical AMD processing could be regulated by applying controlled oxidative agents in coal mine tailings, i.e., ozone and hydrogen peroxide, so as to greatly accelerate bio-oxidation and therefore to mitigate, in the relative short term, mobilization/leaching problems by achieving the extinction of AMD processing causative sources. Selected agents demonstrate high oxidation potential, and no harmful residues are to be formed when they undergo decomposition during treatment [185]. Subsurface propagation of the oxidative agents employed and the active plume formed were monitored by using well-set up mathematical models [186].

A conservation equation was used in a porous medium, performing variable saturation along with convection, i.e., diffusion and dispersion coefficients of liquid gas phases. Brinkman equations were adopted for porous medium flow. Finite element simulations were achieved by using COMSOL Multiphysics^® for the final solution. The permeability was determined using the well-tested Kozeny–Carman model [187], the dispersion by coupling Richards’ equation [100] and the van Genuchten [80] retention model. Propagation models applied in the subsurface of coal mine tailing piles are based on the kinetic rate estimated of the agents’ consumption and bacterial activity acting as catalyst. Abiotic pyrite oxidation is correlated with the surrounding redox potential (E_h) [188].

Hydrogen (H₂) is a versatile and carbon-neutral energy fuel produced by various methods, such as electrolysis, gasification, steam methane reforming (SMR), etc., and very promising for covering future energy demand. Nonetheless, certain conventional storage barriers render geo-storage alternatives an attractive option since it ensures high storage capacity, comparably low-cost investment and exploitation viability, enhanced safety, high energy storage density, etc. Salt underground caverns, which serve as natural reservoirs, seem to be a fine selection incorporating many significant advantages. Suitable geoformations of such a kind are located worldwide, facilitating safer energy storage planning.

Li et al. (2020b) [189] introduced an upward dissolution rate model, simulating H₂ geo-storage in salt caverns. It entails finite volume and structural dynamic elastic mesh methodology via C++ programming. Furthermore, Wang et al. (2021) [190] developed a new prediction and optimization leaching parameter model of solution mining under gas (SMUG). Certain parameters, i.e., nitrogen volume gas–brine interface depth, leaching rate, water and nitrogen injection pressure and leaching rate play a crucial role in the final accurate prediction outcome.

AbuAisha et al. (2019) [191] modeled H₂ migration to the surrounding rock domain by applying Darcian percolation and Fickian diffusion concepts. The model coupled thermodynamic and hydraulic-driven transport mechanisms and drew the conclusion that van Genuchten’s model parameters were overestimated and H₂ mass loss towards rocky formations was proved to be insignificant given certain pre-assumptions [192].

4.2. Modified Soil Medium

The PHREEQC computer code program [193] simulates leaching curves of experimentally modified soil columns (see also Section 4.1). Sewage sludge was amended to experimental calcareous soil. The same soil specimen tested was enriched with injected heavy metals and nanoparticles of ZnO and MgO and zeolite functioning as absorbents. Simulation program inputs comprise four modules, i.e., SOLUTION, EQUILIBRIUM PHASES, EXCHANGE, and SURFACE. The columns of the enriched soil were incubated for 7 days, and leaching experiments that lasted 18 days were conducted by employing two fixed leaching solutions made of CaCl₂ and diethylenetriaminepentaacetic acid (DTPA) in predefined conc. The PHREEQC simulation program employs organic surface complexes. Heavy metal Log K_s values were extracted from SHM and NICADONNAN databases [181]. Modified soil column responses were studied against leaching solution, and more specifically, the leaching tailing of cadmium (Cd), nickel (Ni), copper (Cu) and zinc (Zn). The SOLUTION module received combinations of mixed CaCl₂ and DTPA solution of a determined concentration equilibrated with solid phases received from MINTEQ. The latter is a software program that simulates heavy metal transfer on account of the pre-prepared mixture solutions and solid-phase interaction. Heavy metal propagation was simulated by means of absorption/complexation of MgO, ZnO, and zeolite serving all as reactive sites. Ion exchange sites are simulated by the EXCHANGE module and heavy metal transport by the TRANSPORT component. Monitoring cell (individual grid) and leaching time were properly defined for the running simulation [194].

As a result, the PHREEQC displayed a respectable capacity to simulate the leaching of heavy metals through modified soil columns well prepared to undergo lab-scale testing, though in earlier years [195] there have been experimental mismatches against PHREEQC predictions. Input data extracted from databases refer to pure solid phases, which is not our case in the conducted experiments. Therefore, mismatches are to a great extent justified, since leaching rate by simulation was highly dependent on the SI and the solid phase type. The use of different soil types entails deeper study of surface reactions and ion binding.

In the bibliography, the PHREEQC code simulates the experimental results from heavy metal leachates derived from various waste forms and sewage sludge [196,197,198]. It is suggested that the cation exchange reaction is the predominant mechanism of Cd transport in the soil profile. PHREEQC predicts heavy metal simulation leaching well, e.g., Pb, in modified soil, taking into consideration ion exchange mechanisms and surface complexation reactions [199].

Electric power research institute (EPRI), an independent non-profit energy research, development, and deployment organization, adopted the MINTEQ approach model to develop the FASTCHEM geochemical hydrodynamic solute transport model for modeling coal ash leachate dispersion and advection. It demonstrates useful appliances over heavily polluted soils by fly ash dispersion derived from fossil fuel power plant operations [200].

The RZWQM2 (1-D) point scale model was tested over cultivated soils and soils enriched with slurry, mostly sandy and sandy loam quantities. In all cases studied, predictions were made for soil mineralization, ammonia gas and N₂O emissions, and nitrate leaching regarding testing of each individual soil type. The scope of the experimental effort was to set up integrated strategies over nitrogen gas abatement derived from livestock farming activities and the prevention of nitrate leaching phenomena on the ground [74].

The application of agri-residuals over cultivated soil and inclined terrain farms is a common practice to ensure higher crop yield, to minimize erosion phenomena, and to increase water soil infiltration and retention along with the improved evaporation characteristics. Wheat straw mulching or rapeseed oil residue improves rainfall infiltration outcome. Experiments conducted by employing classic Horton, Kostiakov and Philip infiltration models combined with evaporation models by Rose and Gardner indicated that water retention results regarding mixed soils with agri-additives were significantly improved. Effective water retention techniques may be developed based on how the direct straw integration types correspond to soil infiltration and evaporation. Experimental research demonstrates that mixed straw mulching improves soil water response by increasing infiltration, improving sediment yield, and reducing runoff. The former is especially helpful for implementing integrated ecological management over agricultural regions, such as arid/semi-arid regions with limited water resources, like China [201,202].

4.3. Cement Leaching Medium

Zielina et al. (2022) [203] proposed a mathematical model to predict heavy metal leaching through fresh mortar-lined porous cement Portland cement (PC). Leaching takes place in water under dynamic conditions, taking into account sorption phenomena apart from those already applied in the literature, i.e., dissolution, diffusive and advective transport. The safe prediction of heavy metal concentration at the ends of drinking water supply pipeline sections will meet all necessary actions for the suitable rehabilitation by cementation in accordance with the European active legislation [204] water quality conc. intended for human consumption [203].

PC’s basic constituents are oxides, mainly CaO, SiO₂, Al₂O₃, Fe₂O₃, etc. Certain heavy metals, i.e., Cr, As, Cd, Pb, are inevitably part of the final cement production, derived from various sources, which potentially have a negative effect when accumulated due to their high toxicity to human health and ecosystems. (PC) underwent coupling during hydration, and leaching tailing kinetics of the four aforementioned metals and metalloids were tested over different (PC) specimens [205]. Earlier research was conducted on iron leaching from steel or cast-iron models, dependent on physicochemical parameters [206], and copper leaching via hydrodynamic processes, including the presence of biofilm [207].

The heavy metal kinetics equation is based on the Elovich empirical equation. It was selected and tested, slightly modified, since it can reflect adsorption and desorption processes of heterogeneous chemical reactions. Constants of the equation reflect the diffusion rate of heavy metals from solid to liquid and the rapidness of the diffusion rate. Furthermore, the selected Freundlich dynamic equation simulates adsorption and desorption kinetics of ions and heavy metals in soil and deduces the correlation coefficient of the adsorption process. Finally, the second-order kinetics equation was also preferable over others of the same kind since it satisfactorily describes the reaction rate and ion concentration in the equilibrium state, and the parabolic equation expression depicts the ion release process, controlled by multiple diffusion mechanisms [205].

4.4. Landfill Capping Layers

Numerical modeling techniques efficiently predict leachate generation [208] especially determining parameters of leachate collection, drainage systems, etc. [209]. The hydraulic evaluation of landfill performance (HELP) [210] is a deterministic, widely used, quasi-two-dimensional hydrologic model. It combines (1-D) soil physical and hydrological processes, both in saturated and unsaturated vertical flow, and towards the lateral direction (i.e., lateral drainage). Model run requirements are certain data to be collected, i.e., saturated hydraulic conductivity, soil water retention characteristics, actual meteorological data, solar radiation, leaf area index, evapotranspiration, surface runoff, and the interflow [211]. The model simulates water vertical flow through up to four types of landfill layers [77].

Other models evaluating from hydrological aspect landfills are UNSAT-H [212], HYDRUS-1D [213] and the finite element subsurface flow system program (FEFLOW) [214]. HELP also incorporates evaporation, infiltration, runoffs, and lateral drainage [215]. Input data for the model running are climatic (i.e., temperature, wet precipitation, solar radiation), soil characteristics (i.e., porosity, hydraulic conductivity, field capacity, wilting point), layer arrangement (i.e., surface snowmelt, surface runoff, interception or rainfall by vegetation, evaporation), vegetation. The model comprises surface (i.e., snowmelt, rainfall, interception of rainfall by vegetation, surface runoff, evaporation) and subsurface processing (i.e., soil–water evaporation, vertical drainage, plant transpiration, lateral drainage, liner leakage) [77]. The soil profile was divided into smaller profiles in order to facilitate computation.

Leachate prediction of landfill capping soil profile can be achieved by employing robust integrated artificial intelligence combined with the use of GWO algorithms and the support of ELM [14] (see also Section 3.5) for predicting landfill leachate quality (COD and BOD₅) and groundwater quality (turbidity and EC) at the Saravan landfill in the Rasht region, Iran. Many other models and components are of minor importance, and more information is shown in

Table 1. Water solute leachate models as prediction tools for surface and subsurface soft water and crop change management (not all mentioned in the corpus of the text) and related information.

Model or Platform/Type	Pressure Drivers/Application	Porous Medium	Data Collection/Input	Reference
ADAPT, (extension of GLEAMS with DRAINMOD hydrological component)	Agricultural subsurface drainage for nutrient transport/and macrospore flow transfer.			[137,176,216]
AGNPS/non-point source model, (lumped conceptual type)	Non-point pollution simulation resulting from agricultural activities.	Watersheds		[32,102]
ANFIS	Groundwater quality for irrigation using prediction of irrigation water quality index (IWQI), soluble sodium percentage (SSP), sodium adsorption ratio (SAR), potential salinity (PS), Kelley index (KI) and residual sodium carbonate index (RSC).	Sandstone aquifer	On-site water sampling collection.	[149]
ANIMO/mechanistic model	Nutrient leaching prediction/surface, groundwater quality prediction, agri-environmental indicators testing, nitrogen transformation and leaching.	Root zone		[176,217,218,219]
ANN combined with SES-BiLSTM and SES-ANFIS models, (LMBP) and (MLP) algorithms, ANN combined with fuzzy logic	Water table depletion, saltwater intrusion wedge, water quality prediction in different groundwater, groundwater level prediction.	Groundwater	On-site water sampling collection, preprocessing (SES) method for weight of the dataset, and models’ output adjustment.	[12,13,141,148]
AnnAGNPS	Phosphorus and nitrogen transport.	Watersheds		[220,221]
ANSWERS/lumped conceptual type	Watershed and soil nutrient planning.			[102]
ANSWERS 2000 (incl. Green and Ampt infiltration model)	Catchment scale, surface runoff and sediment transport model, sediment loss.	Water, soil	Operational time step flexible, e.g., during runoff.	[222,223]
APEX/single porosity approach	Sediment and phosphorus loss estimation, phosphorus contribution to tile drains, management practice effects simulation on runoff, sediment, and phosphorus loss.	Macropore soil, forestry		[224,225,226]
APSIM various versions, biophysical, unsaturated zone model, incorp. modules for simulating specific crops, (use of Rosetta and PAWCER model)	Nitrate dynamics leaching in irrigated croplands/crop yield and N uptake, nitrate leaching control, simulate impacts of environmental and agricultural management factors on deep drainage and nitrate leaching, controlling deep drainage and nitrate leaching.	Crop field, paddock scale	SurfaceOM, SoilN, SoilWat, Canopy, Crop modules, soil properties data for particle size analysis, irrigation scheduling, annual rainfall, soil moisture content and chemical properties, runoff, soil evaporation, saturated hydraulic conductivity, water flow and content parameters, fraction of inert carbon estimation, C:N ratio, organic matter content, air and dry water content, soil texture, drained upper limit.	[103,104]
AquiMod/Lumped Conceptual Model	Groundwater level prediction tool.		Groundwater level time series.	[33]
AqYield/AqYield-N, Nitrogen oriented variant	Nitrogen leaching/field scale, management for mitigating environmental nitrogen losses, crop model N leaching.	Crop soil	Soil properties, daily climate features, sowing & harvest dates, irrigation, soil tillage depth.	[56,57]
Biome-BGC, biogeochemical ecosystem model	Soil carbon and nitrogen fluxes, soil water storage, net primary productivity, transpiration, soil respiration, nitrogen mineralization and leaching prediction, net ecosystem exchange, key indicators for ecosystem quality status.	Global scale model	Soil texture, depth, elevation, meteorological data (e.g., wet precipitation, temperature), local physiological parameters (e.g., canopy, limitation of light penetration, maximum photosynthetic rates, leaf carbon to nitrogen ratio, lignin proportion of dead wood).	[91,92,94]
BRANN/type of ANN	Prediction of groundwater quality levels.	Ground water model		[12,16,227]
CALF	Herbicides dynamic estimator.			[144]
CAMEL	Diffuse transport sources of reactive phosphorus/phosphorus identification at critical source area.	Catchment scale		[228,229]
CENTURY/process-based monthly time step model, DeyCent is the daily time step counterpart	Crop growth simulation.	Soil carbon (C) and Nitrogen (N) dynamics	Soil Organic Matter (SOM) and litter pools with different (C:N) ratio and decay rate.	[86,230]
CERES-Maize	Crop growth simulation.	Crop soil	Weather data, solar radiation, soil texture, bulk density, plant growth parameters.	[18]
CoupModel/bio-geophysical, process-based, multi-component ecosystem model	Fertilizing optimization in croplands. C, N dynamic cycles of terrestrial ecosystems.	Agricultural soil	Soil organic matter, vegetation biomass, soil, weather and N deposition data.	[110]
CREAMS	Field-scale chemicals /runoff, and erosion model.			[27]
CROPGRO-Soybean	Crop growth simulation.	Crop soil	Weather data, solar radiation, soil texture, bulk density, growth parameters.	[18]
DAISY ver. 4.01	Nitrogen leaching/cropping strategies affected by nitrate leaching, agri-environmental indicators evaluation, precise fertilization.	Agricultural soil	Soil hydraulic properties, climate data, soil texture, crop management.	[95,101,128]
DayCent/mechanistic model, multi-layer soil division, a daily version of CENTURY	Nitrogen cycle in soil for various ecosystems.	Cropland and forest soil	Soil and topographic properties/hillslopes, spatial distribution of land use types, daily meteorological data, plant parameters and nutrient amendments.	[44,45]
DNDC	Nitrate leaching in crop field, aquifers’ nitrification/, modeling nitrate leaching in crop fields, carbon sequestration and nitrogen denitrification estimation.	Crop field soil	Coupled with a biogeochemical model, crop yield datasets.	[37,38,40,43,117,118,231,232]
DRAINMOD/deterministic hydrological model	Agricultural subsurface drainage for nutrient transport, groundwater salinity problems/groundwater flow under shallow water table conditions, rising water table control, transformation of nitrogen in a stream flow.	Field scale, cultivated soil, soil profiles		[16,135,136,219]
DRAINMOD-NII	Nitrogen cycle dynamics prediction.	Shallow water table soils	Decomposition rate and C/N ratio, kinetics rate constants, N diffusion coefficient in the gaseous phase.	[136,137,219]
DRAINMOD-P	Agricultural drainage for phosphorus transport/phosphorus cycle dynamics prediction.	Artificial, agricultural, forest soil		[138,176]
DRASTIC/Adjusted DRASTIC Model (DRASTICA)	Groundwater vulnerability, soil-solute leaching factors control on regional scale and prediction, land use management.	Groundwater at a regional scale	GIS based, depth to groundwater, soil properties, topography	[15,104,233,234]
DSSAT (crop growth module)	Crop production simulation over time and space for different purposes.	Cropland soil	Soil, crop, weather, and management input data.	[70,161]
ECM	Nutrients’ load to surface water, prediction of total (N, P) delivered to surface water.		National environmental databases/geoclimatic region typology.	[19]
EcoMod (agro ecosystem model)	Nutrients’ fate, leaching/adsorption, ammonium nitrification, gaseous (N2) losses. It quantifies the pastoral ecosystem responses to climatic and soil variability, animal type selection for pasture, irrigation and fertilizer application.	Pastoral soil ecosystem	Stochastically created 99-year climate files (Stochastic Climate Library), pasture growth date, animal’s physiology and feeding, water and nutrient dynamics in soils, calculations for light interception and photosynthesis.	[34,35]
EPIC	Soil erosion/erosion and productivity calculator, erosion’s effect on soil productivity and final assessment.	Agricultural soil		[124,125]
EVACROP 1.5, updated version EVACROP 3.0 percolation model	Nitrate leaching in crop field, aquifers nitrification/cultivation yield, optimization with catch crops.	Crop field soil	Grain equivalent factors.	[108,109]
FASTCHEM, geochemical hydrodynamic solute transport code based on MINTEQ approach	Fossil fired power plants pressure on soils, flying ash leaching attenuation in soils.	Soil–flying ash interaction		[200]
FEFLOW/Finite Element Subsurface Flow and Transport Simulation System	Predicts leachate flow and transport, landfill hydraulic stability prediction.	Landfill capping	Saturated hydraulic conductivity, soil water retention characteristics, actual meteorological data, solar radiation, leaf area index, evapotranspiration, surface runoff and interflow.	[211,214]
FRAME (coupled unsaturated flow model SIWARE and a groundwater simulation model SGMP)	Irrigation water management model.	Groundwater basins		[16,235]
GEPIC/spatially distributed	Crop-soil nitrogen dynamics simulation, optimal fertilizer allocation simulation, groundwater quality standards compliance.	Cultivated land/regional scale		[236,237,238]
GLEAMS (inc. hydrol. erosion, & pesticide component)/lumped conceptual	Agricultural subsurface drainage, nutrient transport, fate of agricultural chemicals/water quality evaluation prediction, agricultural management plant root zone control.	Field-size area soil		[28,29,30,239,240]
GLYCIM	Soybean growth simulation model.			[89,241]
GOSSYM/mechanistic two-dimensional (2D) gridded soil model, incorporates many routines as components, coupled with expert system GOSSYM-COMAX, GOSSYM-2DSOIL	Soil-nitrogen pollution, soil-herbicides pollution, /cotton crop growth and yield, COMAX an inference incorporated engine for cultivation practices, fertilizing regulation, water, carbon and nitrogen interactions in soil, plant root zone and crop response to climate variables and water irrigation.	Cultivated soil	Daily weather information, crop maturity, soil condition, plant growth data.	[18,89,90]
HELP/deterministic model, statistical-empirical, simulates water vertical flow through landfill layers	Landfill’s leachate assessment, hydrological evaluation, landfill’s leachate generation prediction.	Landfill capping and subsoil layers	Climatic data (evapotranspiration, temperature, wet precipitation and solar radiation), soil type, vegetation, capping design and layers’ arrangement.	[77,210,211]
HSPF/solute hydrological simulation/catchment-scale water quality model	Modeling phosphorus transport/field scale runoff model.	Humid subtropical agricultural fields, alluvial plain		[240,242,243]
HAIM with ELM GWO algorithm	Landfill leachate to the ground/landfill sites monitoring.	Landfill sites	Leachate series quality data.	[14]
HGS/Integrated modeling platform process based (including Richards eq.), (finite element, fully integrated numerical model)	Solute transport/hydrological model, solute and pollutant transport. It simulates coupled 3-D variably saturated, subsurface flow and 2-D surface water flow, snow accumulation, snowmelt, and evapotranspiration.	Agricultural soil, forests, catchments, regional scale model	Applied along with EauDyssée, surface-water mass balance module, provides inputs when coupled with (HGS).	[244,245]
HYDRUS-1D/process based, HYDRUS-3D/finite element model	Solute infiltration, dynamic leaching flux and soil water storage including dissolved CO2 and N2O concentration, nitrogen leaching, landfill’s leachate fate/water, heat and solute transport model, hydrological evaluation.	Variably saturated porous media e.g., landfill capping	Calibration before use, evaporation, plant transpiration, meteorological variables, irrigation, soil nitrification and denitrification, soil hydraulic characteristics, use of pedotransfer functions.	[71,72,77,79,82,83,213]
HYPE (Semi-distributed hydrological model)/E-HYPE	Nitrate losses/drainage and water quality processes, introduction of hydrologic response units to segregate the control area.	Croplands/various		[246,247]
ICECREAM (inc. Richards eq.)/ICECREAM-DB, plot scaled model	Simulation of P transport, water discharge and erosion, phosphorus losses quantification.	Soil profile, dual porosity, macroporous soils		[176,248]
IHACRES/IHACRES Classic Plus	Rainfall and runoff simulation, surface hydrologic processes using spatially varying data.	Catchments		[249,250]
IMS, includes components (UTHBAL), (UTHRL), (MODFLOW), (REPIC), (SEAWAT)	Coastal waterbodies salinization, integrated coastal waterbodies management applied on basins.	Croplands, coastal watersheds, river basins, coastline aquifers (east Mediterranean region)		[120]
INCA (Integrated Catchment model), process-based semi-distributed dynamic model/INCA-N nitrogen oriented/INCA-P phosphorous oriented/mixed model	Phosphorus and nitrogen leaching estimation/phosphorus dynamics prediction.	Catchment scale		[251,252]
ISSM (comprises SWAT, MODFLOW and MT3DMS and QUAL2E).	Water and nutrients leaching prediction from surface to the aquifer level, groundwater dynamics, aquifer interaction with the stream system, surface water and nutrient fluxes.	Watershed soil		[128]
ITS, groundwater model	Prediction of groundwater level.	Ground water model		[16,227]
LASCAM/conceptual model	Nutrients’ leaching, nutrient mobilization and transport estimation.			[240,253]
LEACH/LEACHM/LEACHC/LEACHP/LEACHW	Water and Solute Movement, process-based model of water and solute movement, transformations, plant nutrient uptake and chemical reactions prediction.	Soil unsaturated Zone		[75,144]
Leaching release kinetics (modified Elovich curve, Freundlich dynamic eq., parabolic eq., 2nd order eq.)	Heavy metal leaching/leaching phenomena prediction.	Portland cement		[205]
LISFLOOD/physically based model	Rainfall and runoffmodeling within a GIS controlled frame.	River basin		[254]
LPJ-GUESS/LPJ-GUESS LSM	Land use investigation combined with climate change.	Vegetation soil at a terrain grid level up to 1 km2.	Data derived from common agricultural policy regionalized impact (CAPRI) model.	[84]
MACRO/1-D mathematical model, (two-domain process GSmodel, i.e., micro and macropores)	Pollutant transport, phosphorus leaching, herbicide leaching, chemical agents transport estimation, water flow and solute transport, macropores are considered to be pathways when non-equilibrium flow is the case. The model represents lateral flow to drain using suitable sink terms.	Cropland and forest soil (silt, loam soil), macroporous soil.	Soil water content and soil temperature, air temperature and rainfall, herbicide losses measurements.	[255,256]
MAGIC lumped-parameter analytical model	Surface water model of intermediate complexity, predicting long-term effects of acidic deposition on soil and surface water chemistry.	Soil and soil-water catchment		[257]
Mathematical Numerical model using Darcian percolation and two-phase Fickian diffusion	Prediction of H2 Transport in salt cavern.	Saturated rock salt	Thermodynamics, transport mechanisms.	[191]
MESSAGE	Fertilization appliance simulation. Integrated assessment model, trade-off between crops yield and nitrogen for various regions.	Crop soil	Wheat and maize yield.	[85]
MIKE SHE/(coupled with DAISY), 3D physics-based model/finite difference, coupled with MIKE-11	Nitrates leaching groundwater contamination, nonpoint nitrate contamination, due to agricultural activities/It simulates overland and channel flow along with solute transport in the unsaturated zone.	Catchment scale		[102,251]
MIKE-11/1-D hydrodynamic model	DO, BOD, NO3−, NH4+, coliforms/P-water quality parameter estimation			[19]
MINTEQA2 (geochemical thermodynamic equilibrium model/database) EPA-USA	Equilibrium model for diluting heterogeneous aqueous systems.			[184,200]
Model with incorporated Richards eq., van Genuchten parameter expressions, traverse isotropy for sedimentary rocks	Barren ore leachates, propagation model of oxidative agents/accelerated AMD and leachate tailing prediction	Coal mining waste	Soil water saturation	[185,186]
MODFLOW/combined with SWAN (SWATMOD)	Groundwater flow.	Ground-water		[16,67,69,258]
MODFLOW-GRASS, finite difference groundwater flow model, coupled with GIS module GRASS	Large scale groundwater flow.			[259,260]
MONERIS/semi-empirical, conceptual model/semi static	Total N, P, heavy metals and some priority substances prediction/Support environmental studies/Freshwater ecology and inland fisheries prediction tool.	River systems	Runoff-off water quality and spatial (GIS) data.	[19]
MOSFLA/modified, coupled to SWAT	Farm soil management tool.	Farm soil	Shuffled frog leaping algorithms, a farm-level economic model, cost estimator (FEM).	[66,237]
MT3DMS/modular 3-D transport model	Groundwater contaminant leaching/nitrate pollution aquifer’s nitrates transport.	Groundwater Systems	SEAWAT and MT3DMS employ similar boundary conditions.	[120,126]
NIT-DRAIN conceptual nitrate model	Agricultural subsurface drainage for nutrient transport.	Croplands	Subsurface drainage discharge measurement and water quality parameters at the catchment outlet.	[87]
NLEAP/mechanistic model, coupled with GIS data NLEAP-GIS, (version 4.2)/with ANN, genetic algorithms utilization	Nitrate soil leaching, Nitrogen losses to the environment especially in combined cropping landscape/N losses assessment below root zone of crops, applied over risky landscape and cropping system combinations, economic analysis, use of criteria, useful of management practices over soil nitrogen transform and mitigation.	Risky landscape and cropping lands		[113,115,116,119]
NLES5/NLES4/empirical model, exponential function	Nitrate leaching in soils/Estimation of nitrogen input to cultivated soil and crop sequence planning, nitrate leaching from the root zone of agricultural land.	Cultivated soil	Nitrogen leaching calibration datasets, winter vegetation, soil content.	[98,131]
NTRM	Soil nitrogen pollution/management	Soil profile	Weather data, soil properties, crop characteristics, daily biomass and leafage extended area.	[261]
Numerical model, 3-D evolution of a horizontal cavern	Safe H2 geo-storage/multi-step leaching	Composite structural mesh	Brine concentration	[189]
PAPRAN/Nitrogen dynamic of soil-plant systems, pasture model	Simulation model of annual pasture production limited by rainfall and nitrogen	Pasture terrain		[262]
PATRICAL/a distributed model	Anthropogenic eutrophication of agricultural fields/nitrate concentration estimation in aquifers and surface water after nitrogen appliance on crop soil.	Agricultural fields	Hydrological and water quality data derived from surface water and groundwater monitoring network.	[129,130]
PELMO	Pesticide leaching/pesticide fate prediction model and worst-case leaching scenario.	Soil profile		[144]
PESTDRAIN	Pesticide soil drainage/pesticide leaching dynamics of drained soil profiles.	Croplands, soil profile		[87,263]
PHREEQC/PHREEQCRM	Heavy metal leaching, mineral is likely to dissolve or precipitate in groundwater/heavy metal leaching simulation in contaminated soils treated with sewage sludge in the presence of various adsorbents and SI estimation.	Sewage, sludge-amended soil, geo- and nanomaterials, zeolite, pyrite and ash contaminated soils	Solution equilibrium phases, inputs exchange, use of VMINTEQ, NICADONAN, and SHM databases, MINTEQ thermodynamic database.	[178,183,193,194,264]
PLASM/digital groundwater model	Groundwater pressure/simulates the seasonal behavior of groundwater basins, planning and management.	Groundwater basins		[16]
PLEASE/conceptual, plot scale model	Phosphorus losses estimation.	Soil profile, cultivated soil		[265]
PLMP/PDP single porosity models (incorporates four modules) land use partitioning	Phosphorus leaching/Phosphorus dynamic model transport, including precipitation, infiltration, evaporation and runoff.	Lowland polder soils/paddy/dry lands	Daily reference evapotranspiration, crop factors.	[176,243]
PRZM/PRZM3	Pesticide root zone transport, pesticide and nitrogen fate in the crop root/unsaturated soil zones prediction model	Unsaturated soil zones		[144,266]
QUAL2K (1-D steady state model), advanced version of the QUAL2E	Phosphorus and nitrates simulation, suitable for modeling pollutants in freshwater interacting with sediment.		Flow data and hydraulic terms, initial conditions, reaction rate coefficients, local climatological data for heat balance computations, biological and chemical reaction rate parameters.	[19]
REPIC (coupled EPIC model and R-ArcGIS)	Agronomic, nitrate leaching model/crop growth	Soil profile for cultivated soil		[238]
RNN (type)				[159]
RT3D	Contaminant transport model			[69,251]
RZWQM, (release. 2007, RZWQM2)/simplified empirical plant module	Nitrate, phosphorus leachate prediction, aquifers nitrification estimator, developed to simulate the water and nitrate fate for the crops	Cultivated soil, Root Zone, sandy, sandy-loam profiles	Crop empirical model parameterization, meteorological data, soil water content, bulk density, hydraulic conductivity, soil-atmosphere N2O quantified exchange, pesticide concentration, seepage, drainage, annual soil organic N mineralization, soil heat flux, biomass, canopy and plant information.	[74,161,166,167,168,169,170,171,172,173,267,268]
SAHYSMOD (Spatial-Agro-HYdro-Salinity MODel)	Land reclamation/evaluate factors affecting operation and design of bio-drainage system, management scenarios, salt and water balance analysis.	Waterlogged areas	Coupled salinity model SaltMod and groundwater model SGMP/calibration/validation.	[16,269]
SEAWAT simulation of 3-D variable density/generic MODFLOW/MT3DMS-based computer program	Aquifer salinization/ground-water quality monitoring, sea water intrusion.	Coastal soil profile	Time-series of crop yields, groundwater table observations, observed concentration of nitrates and chlorides, SEAWAT and MT3DMS employ similar boundary conditions	[120,127,238]
SGMP/finite difference method	Groundwater model			[16,235]
SIMCAT /stochastic, deterministic, Monte Carlo analysis technique	High values DO, BOD, NO3−, Cl−, NH4+			[19]
SIMGRO/physically based model	Simulates water flow in saturated, unsaturated zone and in surface water.	Regional hydrological model		[16,270]
SMILE/SIMPLACE	Simulation for sustainable crops and agroecosystems.	Crop soil and agroecosystems		[271]
SimplyP/conceptual	Phosphorus leaching/dynamic water quality estimation			[252]
SMDR/, physically based	Surface water simulation, fully distributed numerical model			[251]
SOILN	Nitrogen dynamics and losses in agricultural soil, surface, subsurface and soft water quality/N dynamics simulation.	Layered agricultural soil		[105,272]
SOLMINEQ/SOLMINEQ88 (USGS), geochemical model.	/Chemical modeling of aqueous systems	Water-rock interaction		[273]
SOLTEQ/MT3DMS modular 3-D multi-species transport model	Stabilized waste leaching/leaching on solidified and stabilized waste., advection, dispersion and chemical reactions of contaminants simulation in groundwater systems.	Soil profile and groundwater system		[274]
STICS/conceptual, generic	Subsurface drainage modeling, nitrogen and CO2 flux, changes of carbon pool/Soil-crop dynamics prediction model, crop growth and crop N uptake management.	Crop soil, soil profile	Soil-water, nitrogen balance, climatic and agronomic input data, weather conditions, data from cropping practices.	[51,52,53,54,55,56,57]
SVM to support water quality index (WQI)	Degradation of groundwater quality for irrigation purposes/groundwater quality for irrigation usage, prediction of irrigation water quality index (IWQI), soluble sodium percentage (SSP), sodium adsorption ratio (SAR), potential salinity (PS), Kelley index (KI) and residual sodium carbonate index (RSC) estimation.	Sandstone aquifer	On-site water sampling collection, model training, model validation.	[149,150]
SUTRA /finite element simulation model	Water table prevention from salinity, saturated/unsaturated fluid density dependent groundwater flow, used as machine learning models approximation	Waterlogging areas, groundwater flow		[11,16]
SWAP/process based	Solute leaching, soil transport/water-solute and heat transport, plant growth simulation	Plot scale, agricultural soil, forest	High frequency and high-resolution measured data/GIS data	[16,176]
SWAT/Semi-distributed hydrological model, coupled with MODFLOW, incorporates empirical vegetative filter strip model (VFSMOD)/SWAT+	Nitrate losses, agricultural chemical leaching/drainage and water quality processes, prioritizes new sustainable agricultural methodologies and management practices in agribusiness including fertigation.	Croplands, watersheds soils	Subbasin divisions and digital elevation model (DEM) data, soil profile moisture distribution, climate, soils, and land use, surface runoff lag coefficient, point source inputs, pesticides half-life. Complex model incorporates weather generators which downscales monthly climate data to daily required data.	[61,63,65,67,240]
SWATMOD (modified SWAT and MODFLOW components)	Surface water simulation, stream aquifer and groundwater interactions.	Cropland and watershed soil	Spatially varying parameters, algorithms to facilitate the heterogeneity of karst aquifers, stream-aquifer interaction.	[16,76]
SWBACROS	Irrigated water saving/shallow groundwater contribution to the water needs of a maize crop.	Cultivated soil		[16,275]
SWIM/single porosity model	Surface transport of dissolved and particulate P/water quality and quantity simulation, impact of land use, management practices against climate change.	Mixed land use		[104,176]
SWRRB	Watershed, Rural Basins, decision support tool		Daily weather data, basin division	[31,144]
TAM-MO-DEL/conceptual	Soil-solute leaching/water-solute dynamic assessment, leaching from drained soil profiles.	Cropland		[276]
TETIS/process based	Nitrogen leaching/hydrological model, nitrogen cycle monitoring including atmospheric deposition	Cultivated/irrigated soil	Corine land uses, maps and pedotransfer functions, meteo database, FAO organization crop coefficients.	[46,47,50]
TOMCAT/Monte Carlo analysis approach/SLIMCAT	High values DO, NH4+, BOD/Water quality prediction against contaminants i.e., ammonium (NH4), and water quality parameters, i.e., dissolved oxygen (DO), and biochemical oxygen demand (BOD)		Landfills and others.	[19,277]
TOPCAT/TOPCAT NP	Total N & P simulation.	River water bodies	Input of hydrologically effective rainfall, use of moisture stores.	[19,278]
TOPMODEL/topography-based model	Spatial and temporal predictions of soil moisture dynamics, variable source areas, runoff and evapotranspiration.			[279]
TRIPLEX-DOC and modified TRIPLEX-DOC/process-based model	Simulates DOC dynamics, DOC and POC transformation prediction	Monsoon forest ecosystems, temperate forest soils	Soil organic carbon conc., total nitrogen concentration, plant species composition, clay content, pH, soil Fe and Al concentration, daily climate information (i.e., max/min temperature, wet precipitation), soluble C from fresh litter and root exudates.	[59,60]
UNSAT-H	Unsaturated Soil Water and Heat Flow Model	Soil profile		[212]
UZF-RT3D	Nitrates pollution/Evaluate the performance of best management practice of cultivated land, monitoring of nitrates attenuation.	Cultivated land		[237,280]
VADOFT is a 1-D finite-element prediction code	Pesticides fate/Predicts chemical agents’ fate in soil		Pressure, water content, and hydraulic conductivity	[144]
VARLEACH /modified CALF model	Soil-herbicides penetration estimator.	Soil profile	Soil-water content and temperature, climatic parameters, soil depth etc.	[144]
Ref. [190] Mathematical model	Safe H2 geo-storage (solution mining under gas)/prediction and optimization leaching parameters, i.e. temperature and pressure.	Rock salt, salt caverns	Water injection pressure, nitrogen volume, nitrogen injection pressure, and gas-brine interface depth.	[190]
WAVE	Soil nitrogen dynamics	Cropped soil with winter wheat		[162]
WEPP a field-scale model	Soil erosion/Erosion prediction			[240,267,281]
WHAM	Mine tailings and heavy metal leaching.	Mining slurry		[181]

Notes: ADAPT (Agricultural Drainage and Pesticide Transport); AGNPS (AGricultural Non-Point Source); ANFIS (Adaptive Neuro-Fuzzy Inference System); ANIMO (Agricultural NItrogen MOdel); ANN (Artificial Neural Network); LMBP (Levenberg-Marquardt back-propagation); MLP (Multi-Layer Perceptron); SES-BiLSTM (Single Exponential Smoothing Bidirectional Long Short Term Memory); SES-ANFIS (Single Exponential Smoothing Adaptive Neurofuzzy Inference System); AnnAGNPS (Annual Agriculture Non-Point Source); ANSWERS (Area Nonpoint Source Watershed Environment Response Simulation); APEX (Agricultural Policy Environmental eXtender); APSIM (Agricultural Production Systems sIMulator); Biome-BGC (BioGeochemical Cycles); BRANN (Bayesian Regulation Artificial Neural Network); CALF (CAL Flow); CAMEL (Chemicals from Agricultural Management and Erosion Losses); COMAX (CrOp MAnagement eXpert); CoupModel (Coupled heat and mass transfer Model); CREAMS (Chemicals, Runoff, and Erosion from Agricultural Management Systems); DAISY (Danish Simulation Model); DayCent (Daily Cent); DNDC DeNitrification-DeComposition); DRAINMOD (DRAINage MODel); DRAINMOD-NII (see DRAINMOD Nitrogen); DRAINMOD-P (see DRAINMOD Phosphorus); DRASTIC (Depth to water, net Recharge, Aquifer media, Soil media, Topography, Impact of the vadose zone, and hydraulic Conductivity); DRASTICA (see DRASTIC Adjusted); DSSAT (Decision Support System for Agrotechnology Transfer); ECM (Export Coefficient Model); ELM GWO (Gray Wolf Optimization-Extreme Learning Machine); EPIC (Environmental Policy Integrated Climate); EVACROP (EVAporation CROP; FEFLOW (Finite Element subsurface FLOW system); SIWARE (SImulation of Water management in the Arabic Republic of Egypt); GEPIC (GIS-based EPIC); GLEAMS (Groundwater Loading Effects of Agricultural Management Systems); GLYCIM (soybean model); GOSSYM (GOSSYpiuM); GRASS (Geographic Resources Analysis Support System); HAIM (Hybrid artificial intelligence model); HELP (Hydraulic Evaluation of Landfill Performance); HSPF (Hydrological Simulation Program-Fortran); HGS (HydroGeoSphere); HYPE (Hydrological Predictions for the Environment); IHACRES (Identification of unit Hydrograph and Component flows from Rainfall, Evapotranspiration and Streamflow); IMS (Integrated Modeling System); INCA (INtegrated CAtchment model; ISSM (Integrated Surface and Subsurface Model); ITS (Integrated Time Series); LASCAM (LArge Scale Catchment Model); LEACH (Leaching Evaluation of Agricultural Chemicals); LISFLOOD (Two-Dimensional Hydrodynamic Model specifically designed to simulate floodplain inundation); LPJ-GUESS (Lund–Potsdam–Jena General Ecosystem Simulator); LPJ-GUESS/LSM (see LPJ-GUESS Land Surface Model); MACRO (MACRO scale model); MAGIC (Model of Acidification of Groundwater in Catchments); SHE (Système Hydrologique Européen); MINTEQA2 (Metal Speciation Equilibrium For Surface And Ground Water); MODFLOW (Modular Ground-Water Model); MONERIS (MOdeling Nutrient Emissions in RIver Systems); MOSFLA (Modified shuffled frog leaping algorithms); MT3DMS (Mass Transport 3-Dimensional Multi-Species); NIT-DRAIN (NITrate DRAINage); NLEAP (Nitrogen Loss and Environmental Assessment Package); NLES (Nitrate LEaching Simulation); NTRM (Nitrogen-Tillage-Residue-Management); PAPRAN (A simulation model of annual pasture production limited by rainfall and nitrogen); PATRICAL (Precipitation Input in Network Sections Integrated with Water Quality); PELMO (Pesticide Leaching Model); PESTDRAIN (PESticide transport in a Tile-DRAINed field); PHREEQC (PH (pH), RE (redox), EQ (equilibrium), C (program written in Q)); PHREEQCRM (see PHREEQC Reaction Module); PLEASE (Phosphorus LEAching from Soils to the Environment); PLMP (Pesticide Leaching Model Phosphorus); PDP (Phosphorus Dynamic model for lowland Polder systems); PRZM (Pesticide Root Zone Model); QUAL2K (A Modeling Framework for Simulating River and Stream Water Quality); REPIC (R-Gis and Environmental Policy Integrated Climate); RNN (Recurrent Neural Networks); RT3D (Reactive Transport 3D); RZWQM (Root Zone Water Quality Model); SAHYSMOD (Spatial Agro-Hydro-Salinity Model); SEAWAT (SEA WATer intrusion model); SGMP (Soil and Groundwater Management Plan); SIMCAT (SIMulation of CATchments); SIMGRO (SIMulation of GROundwater and surface water levels); SIMPLACE (Scientific Impact assessment and Modeling PLatform for Advanced Crop and Ecosystem management); SimplyP (Simply Phosphorus); SMDR (Soil Moisture Distribution and Routing); SMILE (Scientific Model Integrating pipeline Engine); SOILN (SOIL Nitrogen); SOLMINEQ (SOLution MINeral Equilibrium); STICS (Simulateur mulTIdisciplinaire pour les Cultures Standard) [282]; SVM (Support Vector Machine); SUTRA (Saturated-Unsaturated Transport); SWAP (Soil Water Atmosphere Plant model); SWAT (Soil and Water Assessment Tool); SWATMOD (Soil and Water Assessment Tool MODified); SWBACROS (Simulation of the Water BAlance of a CROpped Soil); SWIM (Soil and Water Integrated Model); SWRRB (Simulator for Water Resources in Rural Basins); TOPMODEL (TOPographic MODEL); TRIPLEX-DOC (TRIPLEX-Dissolved Organic Carbon); UNSAT-H (Unsaturated Soil Water and Heat Flow Model); UZF-RT3D (Reactive Transport in 3 Dimensions); VADOFT (VADOse zone Flow and Transport model); WAVE (Water and Agrochemicals in the soil, crop and Vadose Environment); WEPP (Water Erosion Prediction Project); WHAM (Windermere Humic Aqueous Model). ‘Fertigation’ is the technique of supplying dissolved fertilizer to crops through an irrigation system. When combined with an efficient irrigation system both nutrients and water can be manipulated and managed to obtain the maximum possible yield of marketable production from a given quantity of these inputs.

. Models and countries that were implemented in the past, according to the relevant literature, in the present manuscript are presented in

Table 2. Models and countries that were applied according to the relevant literature. The symbol ‘√’ denotes model implementation in country boundaries.

Model/Countries	Australia	Bangladesh	Belgium	Canada	China	Denmark	Egypt	England	Finland	France	Germany	Greece	India	Iran	Italy	Japan	New Zealand	Nicaragua	Pakistan	Poland	Portugal	Saudi Arabia	Spain	Sweden	Taiwan	Tunisia	USA
ANFIS							√
ANN					√								√	√								√
ANN-AGNPS																											√
APSIM	√
Aq-Yield										√
BIOME-BGC					√
BRANN					√
COUP MODEL																								√
DAISY						√									√
DAYCENT					√																						√
DNDC																											√
DRAINMOD-NII														√
DRAINMOD-P																											√
DRASTIC/ DRASTICA					√											√
ECOMOD	√																√
EVACROP						√
FEFLOW											√
FRAME													√
HAIM														√
HELP											√									√							√
HGS				√
HSPF																											√
HYDRUS					√
ICECREAM									√															√
IMS												√
ISSM															√
ITS					√
MACRO								√																√
MAGIC																											√
MIKE SHE						√
MODFLOW		√	√									√	√					√							√	√	√
NIT-DRAIN										√
NLEAP/GIS				√	√
NLES5						√
PATRICAL																							√
PDP					√
PHREEQC/PREEQCRM																			√
PLASM													√
PLMP					√
RZWQM/RZWQM2																					√						√
SAHYSMOD													√
SEAWAT
SGMP												√	√
STICS										√
SVM							√
SWAP													√
SWAT																											√
SWATMOD																											√
TRIPLEX-DOC					√
TETIS																							√

and Figure 6. Furthermore, model advantages and performance drawbacks are shown in

Table 3. Model advantages and drawbacks according to the relevant literature as a result of their implementation.

Model or Platform/Type	Advantages	Drawbacks
ADAPT	DRAINMOD-NII and ADAPT demonstrate the same performance as regards soil water N leachate
ANFIS	Combines ANN and fuzzy inference system advantages.	Long training time before implementation
ANIMO	SWAP combined with ANIMO results in a more realistic simulation of P transport.
ANN	AI reduces the time needed for data sampling and enhances identification ability of the nonlinear patterns of input and output, is more reliable compared to the other classical statistical methods, and demonstrates high accuracy in groundwater level management. Deep learning or unsupervised algorithms are more accurate. ANN models incorporate the most popular algorithm due to their high accuracy, implementation easiness, and input parameters flexibility.
ANSWERS2000	Simulate surface transport of both dissolved and particulate phosphorus.
APSIM	Validated extensively. A specific simulation module is developed for sugarcane.
AquiMod	Unconfined aquifers/run quickly and efficiently to simulate groundwater levels for contrasting aquifer types.
AqYield/AqYield-N	Simplicity, few inputs requirement, prediction with limited data, sufficient estimation, equal accuracy compared to STICS, no pests or diseases are under consideration. The yield and soil water content for irrigated crops are equally well predicted. Mondel entails microbial transformations of N and C.
Biome-BGC	Numerous studies across variant biome types were implemented worldwide. It underwent validation in Tibet.
BRANN	Effective to improve model network generalization by controlling and penalizing large weights of model parameters.
CAMEL		Lack of published validation with field data until 2020.
CENTURY	Wide appliance range over agroforestry and land-use systems e.g., tropical and temperate forests, grasslands, croplands, and agroforestry systems. It is highly adaptable.	Requires many input parameters, difficult to measure or estimate with precision. Input parameters and assumptions with high sensitivity, which incur uncertainties into the results.
CoupModel		Runs on a daily time step.
DAISY	Validated on national scale in Denmark
DayCent	Enabled to simulate sorbed and labile soil-P, tested for satisfactory simulation in mixed landscape and hilly of mountainous terrain.	Computationally intensive, not easy to apply on large-scale spatial and temporal domains, problems with nitrogen dynamic cycle in arid and semi-arid soil, daily time step.
DNDC	Wide range of agronomic and environmental indicators in various agro-environmental conditions.
DRAINMOD		Too many input parameters and measurements with high accuracy at the field-scale, restrictions of appliance on artificial drained lands.
DRAINMOD-NII		Great number of input parameters, high accuracy measurements at the field scale.
DRASTIC/DRASTICA	Fuzzy logic methods with ensemble learning demonstrate better performance.
DSSAT	DSSAT module v.4.0 was linked to RZWQM2 for better crop production. It incorporates N fixation module
EcoMod	Suitable for grazing ecosystems, pastures in Australia and in New Zealand.
EPIC	CREAMS, GLEAMS and EPIC were the base for SWAT model. Epic has intensive data requirements
EVACROP 1.5/3.0	Developed for Danish climatic conditions, it predicts mineralization occurred from catch crop residues.
GLEAMS	More effective with ANN when linked with DRAINMOD.
GOSSYM/GOSSYM-COMAX/GOSSYM-2DSOIL	Modified GOSSYM gives better net photosynthesis predictions, and soil simulation/transpiration process improvement. The GOSSYM-COMAX is widely validated.
HELP		Aging landfill waste and compression were not recognized, since they affect negatively the leachate prediction (underestimation of the leachate generation) Applicance limitations of vegetation type with certain leaf area index for evapotranspiration estimation.
HSPF	Highly published catchment models.
HAIM/ELM GWO	Different landfill sites applicability, robust alternative to MARS, MLPANN, ELM, and MLPANN-GWO in terms of leachate quality predictability and groundwater quality applications.
HYDRUS-1D/3D	Most commonly employed in landfills with multiple solutes in variably saturated porous media.
INCA/INCA-N/INCA-P	Terrestrial and aquatic appliance.
ISSM	Relies on open-source models SWAT and MODFLOW. It demonstrates application flexibility.
ITS		BPANN models are superior to the ITS in forecasting the groundwater levels.
LASCAM		Unable to distinguish between planting in the recharge areas of each sub-catchment against planting in the discharge zones.
LPJ-GUESS	Global vegetation model for nitrogen leaching.
MACRO 1-D	MACRO explicitly considers macropores as pathways for rapid non-equilibrium flow. It represents the lateral flows to drains by using sink terms. It describes sufficiently pesticide transfers and demonstrates complexity for interacting processes.
MAGIC	Catchment soils with rapid soil-cation equilibrium.
MESSAGE	Make use of drivers such as (Representative Concentration Pathways 8.5). Soil leaching predictability in certain scenarios.
MIKE SHE/+ DAISY	Processes the snowmelt apart from evapotranspiration.
MINTEQA2		Limitations with equilibrium constants for certain temperature values and within certain range of ionic strength. Lack of published validation with field data until 2020.
MODFLOW/+SWAN (SWATMOD)	Inferior accuracy in terms of groundwater level prediction, easy accessibility, user friendliness and versatility. MODFLOW potentially coupled with RT3D.
MONERIS	Priority substances simulation.
MOSFLA/+SWAT	More powerful convergence and optimization ability, four times better management outcome.
MT3DMS	Grid cells, on a monthly step.
NIT-DRAIN	Ability to simulate correctly both flux and nitrate concentrations.
NLEAP/NLEAP-GIS/+ANN	Widely applied and validated in the US, Europe, South America and Canada. When coupled with GIS, increases (N) losses assessing capability in risky landscapes with combined cropping systems. It evaluates more accurately management practices over nitrogen transformation and mitigation.
PATRICAL	Flexible river basin scenarios and time projection.
PESTDRAIN	Adopted as NIT-DRAIN and TAMMODEL, conceptual soil reservoir technique.
PHREEQC/PHREEQCRM	Geochemical reaction & transport model, great ability to simulate heavy metal leaching in contaminated soils and calculate Saturation Indices (SI).
PLMP/PDP		Developed to simulate P dynamics in paddy fields. Simulates only dissolved P and particulate P. Unable to simulate transport of particulate P in surface water and dissolved P when runoff occurs from dry and paddy lands. Overcome problem by PDP with USLE and INCA-P.
PRZM/PRZM3		Intensive data requirements
QUAL2K	Simulates up to 16 water quality determinants, algal simulation capability (e.g., Chlorophyll-a). It is not stochastic.	Not dynamic (time invariant).
REPIC	IMS/REPIC, overcome problems of variants of the EPIC model, module of reservoir simulation-optimization module calculations on an annual basis, yield estimation of various crops and different irrigation and fertilization scenarios.
RNN	RNN integrated with GIS enables scientists to predict accurately groundwater quality indices and cope with health risk management.
RT3D	SWAT-MODFLOW-RT3D coupling
RZWQM/ RZWQM2		Requires terrain data such as plant heights, rooting depths of randomly selected plants in crop stages, empirical model parameterization for the crop, successfully used in Mediterranean agro-ecosystems for a long period with extended publication reference.
SAHYSMOD		Long-term effect evaluation of alternative management groundwater scenarios.
SEAWAT	Calibrated model in various areas in Greece, with high final accuracy, coupled with MODFLOW for saline intrusion zone cases	Hydraulic conductivity sensitivity may be biased for seawater intrusion cases of coastal aquifers.
SIMCAT		Time invariant
SIMGRO		The coupling of model is difficult if the flow resistance across the boundaries of subdomains is small.
SOILN	Module to APSIM to improve N, C dynamics.
SOLTEQ MT3DMS	Incorporates cement chemistry.
STICS	Widely calibrated.	Daily time step stimulation, prediction with limited data, no pests or diseases consideration.
SVM	Integrated ML model via SVM supervised algorithm and WQI employment improves understanding of water quality assessment.
SWAP	SWAP reported with best performance compared with MACRO and CropSyst in terms of simulated soil water contents.
SWAT + MODFLOW	MODFLOW performs better when coupled with SWAT over complex surface-groundwater interaction analysis, easily coupled with NSE.	Simplistic simulation of groundwater for SWAT.
SWIM		Lack of published validation with field data until 2020, suitable when coupled APSIM–SWIM to simulate shrink/swell soil hydraulic conductivity and runoff.
SWRRB	Return flow, travel time can be calculated from soil hydraulic properties.
TAMMODEL	Reservoir based approach model.
TETIS	Implemented in watersheds of all sizes.
TOMCAT+ Monte Carlo	Easy to merge TOMCAT and SLIMCAT into a single library.	Time invariant.
TOPCAT/ TOPCAT NP		Not to be used for a topographic distribution function.
TOPMODEL		Not to be used for a topographic distribution function.
TRIPLEX-DOC and modified	Good ability to simulate the dynamics of soil water fluxes in forest soils.
UNSAT-H	Most commonly employed in landfill hydrological evaluation.
VADOFT	The code, when equipped with Monte Carlo, enables the better run of multi-parameter scenarios several hundred times and provides stochastic (probabilistic) outputs.
WEPP	Widely used, applied in a variety of geographic regions, capable of modeling complex hydrologic processes.	Requires a significant amount of input detailed soil and topographic data not always available when applied, computationally intensive, therefore time-consuming simulation, primarily focused on water erosion processes.

.

5. Discussion

Great research conducted in recent years has focused on proactive and rehab actions to safeguard surface and subsurface soft water quality and its uses. Med river types suffer all year round due to climate change (prolong drought periods, rare sudden cataclysmic rainfalls) from low water flows and moderate to low water quality levels from the standpoint of bio-physicochemical criteria. Intensively cultivated areas are adding huge quantities of fertilizers, mostly bio-waste from breeding farms, which gives rise to nutrient concentration in surface water basins and watercourses. Aquifers are progressively being nitrified on account of the nitrogen-based fertilizer surplus, applied to the topsoil, which turns into soluble nitrates and ends up in the underlying water table. Apart from nitrate concentration limitation, where water is intended for human consumption, pumping up and using it for irrigation purposes incurs imbalance in the humic part of the topsoil and negatively affects crop yield due to increased salinity.

The alternative use of soil additives enhances crop yield, mitigates nitrate pollution, facilitates remediation methods, improves anion exchange, soil water retention, and soil texture characteristics. Soil additives have their own mechanisms, i.e., promote fertilizer release in a controlled way to meet the metabolic needs of plants [283,284], natural derived or artificially manufactured adsorbents/absorbents, e.g., biochars, zeolites, peat, hydrogels, etc. [285,286]. There have been literature reports on decision support tools, e.g., multi-criteria decision analysis (MCDA) to employ in order to couple LCA with nitrate infiltration models for nitrate soil management [237].

Therefore, well-tested nitrate leaching models, standalone or as a part of an integral modeling package, provide rapid site-specific estimates of N-NO₃ leaching potential below the root zone of crops and the impact of nitrate leaching into groundwater. Models developed within sophisticated integrated model packaging estimate not only the residual nitrate part but also all potential nitrate pool and leaching losses from small plots up to immense catchments of great acreage. They take into consideration cropland soils into subsoil layers under different combinations of meteorological data, soil profile properties, and farming practices.

Strict cropland nitrogen-based fertilization regulations in (kg N ha⁻¹) in Europe compel farmers to resort to alternative cultivating options and lay emphasis on cultivation models’ predictions that change bio-fertilizing practices and support the terrestrial nitrogen balance cycle. The (GIS) component offers a spatial soil database and increases predictability in demanding terrains that demonstrate individual soil characteristics.

Mechanistic models, to a great extent, are employed in the scientific literature to predict quantity and quality of waste rock drainage and the incurred environmental risk. Nonetheless, they demonstrate great uncertainty due to the apparent heterogeneity (e.g., texture, hydraulic, geochemical, etc.) of the waste deposits, which entails a large number of scale-dependent parameters to support the model equations. To address such cases, a combined deterministic and stochastic modeling approach is considered to be crucial to deal with layers’ heterogeneity [80].

Many researchers promote the development of nested catchment models since regional-scale models are inevitably dependent on smaller-scale models, such as those that provide valuable data to boundary conditions. Furthermore, integrated hydrologic models, i.e., models that eliminate boundary definition between surface and subsurface, are rarely applied on a regional scale due to evident computational cost, which negatively affects the model calibration and incurs high predictive uncertainty. Moreover, the estimation of base flow and each water budget component usually requires additional post-processing steps [245].

Considering the effectiveness of ANN applications and AI offspring is marginally advantageous in predicting hydrochemical and hydrogeological parameters, and most specifically, extensively applied to groundwater modeling and prediction. ANN water prediction tools could minimize water quality monitoring stations and propose alternative ways to estimate groundwater level not relying upon geoelectric characteristics [141]. ML models make use of water quality indices for the final water quality assessment [150].

Μeta-research algorithms, e.g., latent Dirichlet allocation (LDA), have recently been employed to scrutinize relevant literature topics and boost quantitative analysis in nutrient water and soil transport processes. Thus, they are valuable for a better identification of the trends and to fill knowledge gaps [251].

6. Conclusions

Nitrogen leachate prediction models yield satisfactory results as a multi-component tool that co-processes data acquired from site characteristics (e.g., soil texture and depth, terrain elevation, meteorological data (e.g., precipitation, temperature, etc.) in long time series. Microbial communities of the soil and eco-physiological parameters (e.g., canopy light level, maximum photosynthetic activity) are taken into deeper consideration as critical paths for nutrient uptake in the seeded plants’ root zone, which regulates nitrogen surplus to be leached to deeper soil substrates. Soil water simulation models are valuable tools for addressing soil nitrogen pollution and contributing soil nutrient decision strategies as regards crop and fertigation management, e.g., APSIM in Australia. Nitrate–water simulation models in soil profiles require a great number of input data, some of which are to be measured with high accuracy at the field scale, a situation that is not always feasible. Thus, dynamic approach model systems were developed to overcome complex processes resulting from numerous interactions.

The vast majority of the models examined were process-based or conceptual models. Nonetheless, empirical prediction models, though rather simplistic and therefore not preferable, demonstrate certain advantages since they do not require extensive calibration database information, which in many cases is unavailable.

Artificial intelligence and machine learning techniques extend even more prediction capability, offering great potential for accurate water quality prediction without time series use acquired from long period measurement and databases. AI combined with ML algorithms enables the analysis of vast amounts of bulk datasets more efficiently than traditional methods and point out unidentified interrelations and patterns that were up to now unnoticed. Thus, predictive capability is enhanced. Other potential improvements are the refinement of already-used empirical and deterministic models in such a way that leachate movement forecasting might be improved. AI technology boosts sensor integration and facilitates real-time monitoring of soil certain characteristics to predict leachate quality and other environmental parameters that affect the prompt soil water integration risk assessment management and policy making. Furthermore, AI eases uncertainty incorporation into models and incurs significant prediction improvements of potential impacts on ecosystems over time. AI tools are flexible when simulating a great variety of checking scenarios, facilitating decision support systems. One more important aspect of AI techniques is the enhanced ability in model validation/calibration by making use of ML techniques, which allow prompt results with fast parameter iteration and less manual effort.

Hybrid structural chemical agents’ prediction models facilitate researchers to encompass even more profound sophisticated tools regarding climatic change scenarios, greenhouse gases in the atmosphere, combined with soil surface temperature, and proceed to climatic analyses, synthetic weather predictions and support more accurate crop assessment yields, countermeasure decision making against extreme weather conditions, secure crop yield, and deeper understanding of crop physiology.

Intense anthropogenic pressure and climate change with prolonged dry spells incur saline wedge penetration phenomena in the coastal low water table, resulting in water quality devaluation and soft water consumption limitations. Coastline water management involves integrated modeling systems that successfully couple surface and groundwater hydrology, reservoir operation, agronomic/crop planning, and nitrate leaching to address aquifer nitrate transport and seawater intrusion and resilient adaptation plans.

Stochastic modeling is widely used as a fundamental approach tool to embed uncertainty in long-term model-based decisions. Therefore, such a methodology should operate like a regulator against policy and decision makers, who should take into serious consideration stochastic model results.